Like, if you killed someone and then fucked off to the next town, wouldn't it be a hugely difficult thing to prove if nobody saw you do it? They didn't have the kind of forensic techniques back then that we do now, so it's not like they could go up to the killer and tell him they'd found his fingerprints and hair samples all over the crime scene like they can today.
This and many other related topics are covered in Trevor Dean's excellent, highly readable book CRIME IN MEDIEVAL EUROPE 1200–1550, one of the books on the AskHistorians reading list: https://www.reddit.com/r/AskHistorians/wiki/books/europe#wiki_middle_ages
Hello, I wrote an answer here that looked at the mechanisms of law enforcement in pre-Conquest England, and the role of quasi-official community groups called tythings in the apprehension of criminals, under a scheme known as Frankenpledge. It also looked at the role of reeves, thegns and ealdormen in the execution of justice.
It's worth noting that within the context of an Early Medieval community, if somebody was found dead and you were suddenly absent from the community, suspicion would almost certainly fall upon you. Assuming that you were a part of the Frankenpledge, the other men of your tything would be immediately responsible for your apprehension, but could call upon the reeve or the ealdorman for assistance. If the 'next town' also fell under that ealdorman's jurisdiction, the men of your tything would be able to call upon the portreeve there for assistance.
I also wrote a previous answer that might be helpful here: