Jurisdiction can be a complicated issue, when dealing with the legal system; however it is not when dealing with common law.

In simple terms within common law, equity law and democratic law, you just need to prove knowledge of, or show you have personal knowledge or subject matter on the issue.

A true constable of the law, not restrained by crown law, would be able to uphold law regardless of the location of the person who has committed the crime.

Police work for corporations, and as all governments are also corporations, with their own separate policies, the police from one corporate jurisdiction cannot cross into another corporate jurisdiction.

This is easily shown within the United States of America, where the criminal needs to get across the state line.