No, in fact the crime rate and number of people arrested grew larger. The Nazis enacted stricter and more wider reaching laws. The new laws on association with enemies of the state, bans on things like drunkenness meant that more and more people were being arrested. The newer laws also meant more women were being arrested as well, but that didn't really pick up until the war started. Interestingly, the only crimes that really decrease by any meaningful number was rape, sexual assault, and sex with a minor. The reason for this is the lack of young men, due to wartime needs and new programs like the Hitler youth.

Third reich in power by Richard Evans is a must read if you are interested in this type of topic.

In addition to what /u/Warband14 is saying, crime also increased dramatically because the incidence of hate crimes skyrocketed after the Nazis took power. They targeted Jews, Gypsies, Homosexuals, and many other minority groups. You can only imagine how this dramatically increased the rate of crime in Germany.

See here for more.

p.s.: April Fools!