Here's the problem: they were barred by Nuremberg Laws from entering places already, a bar would probably refuse to serve them, and most of them would have been deported to concentration camps. They wouldn't be walking around on the streets and would probably avoid any sort of interaction with you.

Alright, by 1943, there were very little Jews left in Germany proper, where Germany was in all practical sense emptied of Jews. However, from 1939 onward, Jews inside Germany saw their liberties drastically restricted. You wouldn't find a "regular" Jew in a bar at night. It's likely you killed someone with important friends.

What follows is necessarily going to be a little convoluted because policing in the Third Reich was a little complex. There are 3 types of regular police and several types of secret or state or paramilitary police forces. The three official police types were the Ordnungspolizei, who were the uniformed police of the Reich, the Kriminalpolizei, these were the detectives, they had been folded into the Sicherheitspolizei, which was the organization under which the Kriminalpolizei and the Gestapo acted. The SiPo, was further folded into the SS-Reichssicherheitshauptamt under the control of Himmler. So, other than the Ordnungpolizei, all the police forces of the Reich were under the control of the SS and even then, it was only a matter of time until all of them were folded into Himmler's portfolio of ministerial duties. In 1941, a murder with racial components could have gotten the attention of any of those agencies.

You are a worker, sure, you are Aryan, but if you were drunk, I'll assume this happened at night. What does that tell me? Well, all Jews had a curfew imposed upon them relatively early and as soon as rationing in Germany began, Jewish homes had very little resources. So, this Jew was out after curfew, had the resources to go out and frequent a bar. This guy was more important than you, regardless of his Jewish background.

So, what exactly is going to happen. For starters, the regular police (Ordnungspolizei) will be summoned and they'll check your documentation and his. They'll promptly establish that he was a Jew and he was out after curfew. If they discover this before you are arrested and sent to a police barracks, they'll most likely let you go. If the police who responded were ardent Nazis... Then they'll call in the detectives. (Kriminalpolizei) The state had been folding in into its police forces ardent supporters of racial and fascist policies, the nazis had two names for it you may happen upon old time policemen or Nazified policemen, no real way of knowing if you are lucky of unlucky... The man was a Jew, he was out after curfew, his family and friends have to be punished. He will be passed over to the Gestapo. That'll most likely happen rather fast. They'll arrest the family and may deport them in short order to the East. Then someone in the SS, Gestapo or Wehrmacht, any influential service really, including Reichministries, is going to be contacted by whoever the Jewish man's patron was. If he had the strings to pull to keep this Jew out of the resettlement program until 1941, he has the strings to get you in trouble. If that Jew was important for industry for some reason or another... You are in big trouble.

Next, the Gestapo, SS or OrPo is going to pick you up, whether or not its from the police barracks is not important. Maybe you are offered a spot in the army on the Eastern Front. Maybe you are shot on the spot. It really all depends on just how important a Jew you just killed and just how important a patron that man had...

Racial policies were one thing but the war effort was paramount. Its probably bad news that you killed someone with the worst racial background but that had the influence to still be out at night and have the resources to have a good time... A lot of this is going to be really hard to pin down as "what definitely will happen" since one of the main themes of police policy in the Third Reich is that they had incredible discretionary powers...

Sources: Networks Of Nazi Persecution: Bureaucracy, Business and the Organization of the Holocaust p. 3, as to the matter of bribery playing an important part in the system and it also states that in many cases, persecution came from the citizenship way before any kind of official policy was put in place.

Holocaust Museum concurs that the Third Reich enforcement of law became detached from the judiciary relatively early.

Law under the Swastika very short read that should confirm much of what I'm saying.

A similar question was asked before. ( Unfortunately without many answers. )

Further to the excellent answers already given, I'd just like to add the following details The Gestapo were not as powerful as history as assumed up until this point. A German citizens experience of them would have been wildly different to a Jewish persons. Eye-witness accounts from German interactions with the Gestapo state that most of them wore civilian clothes and had the demeanor of civil servants. Your man would have most likely found himself mired in bureaucracy, as very often crimes bridged different offices, paperwork would be released by the Kriminalpolizei, then passed to the Ortsgruppenleiter to look at, stamped, cosigned, and so on. Most likely the murder would have been judged as an accident, or as a result of provocation. The mans racial qualities and any connections would undoubtedly counted. I think he would been found innocent, with little or no repercussions.

What you have to understand about the Nazis rise to power is that existing structures of government were more less untouched (albeit "dejewified"). Even though the NSDAP and organisations like the SA and SS were running the show, the regular police, fire department and all manner of bureaucracies you would expect in a german government continued to exist and still had formal authority over everything. When something the SA/SS did violated established principles they would usually just keep their mouth shut about it, or be physically forced to not act, or receive orders from the top to not act, or actually (but rarely) enforce the law. This strongly varied on a case-by-case basis, though.

The interesting thing about the Holocaust is that it wasn't a rather spontaneous "lets grab our machetes and whack them to pieces" kind of genocide, but bureaucratically organized while regular life went along normally. This is tantamount to understanding the power structures governing Nazi Germany: Everything goes along normally, but whatever the Nazi government wanted to do was sacrosanct. By which I mean, the local fire safety inspector inspects all the buildings in the area, except for the concentration camp.

To give you an idea of what I mean: The Nazis would deport jews to the concentration camps by packing them into cattle train cars, but the Federal Railway Agency would write them a detailed bill for everything that happened.

The local balance of power between the new and the old government was very unstable. The Nazis had tight grip on everything, but you'll find (rare) incidents where they really didn't. When they set out to murder jews and torch synagogues on the Rechskristallnacht in 1938 the SA were able to spread their terror as they wished, but when they torched the Neue Synagoge in Berlin-Mitte, local police drove them away and ordered the firefighters to intervene (even though the firefighters had other orders telling them not to). The local chief of police cited landmark protection laws and danger to adjacent buildings and went unscathed. His name is Wilhelm Krützfeld, he came to minor fame because of this - such semi-direct disobedience is very rare.

Now, back to your bar fight. In late 1938, jews were banned from libraries, cinemas, theaters, museum and public swimming pools. Many private businesses like bars and restaurants (but also grocers) banned jews from entering as well. The government introduced a special ID card for jews (which developed into the infamous yellow star in 1941). Most private property was seized, and jews were banned from trading any kind of goods, and from running stores, and from running manufacturing businesses. Jews were prohibited from possessing or using cars. You wouldn't find a jew just casually sipping his beer in a bar, or walking around at night.

But let's say you found a jew in a bar and killed him in a drunken bar fight. The bartender would likely intervene, because you guys are trashing his bar. Now, someone's gonna call the police, and they would arrest you because you just killed a dude. At some point, a few of the local Nazis would notice the story. One of them was probably sitting in your bar, having a beer. Also, it would eventually conspire that the victim was a jew. You would claim self-defense, be released immediately and later acquitted in court. That scumbag jew probably attacked you and had it coming, and nothing of value was lost anyway. Every policeman and every judge would get that line from the Nazi organisations, and they wouldn't disobey that. You'll receive a bunch of praise from the Nazis for stepping up to defend yourself against one of the jewish usurpers, and the few people who disagreed with that would know to keep their mouths shut.