As Mentioned in Episode 151 – Czars of Kung Fu

The doctrine of hot pursuit does allow the crossing of jurisdictional boundaries and arrest on the other side, as well as what would otherwise be a fourth amendment violation. I’m not aware of a case covering pursuit by telephonic teleportation, though. Also, you are correct that it has nothing to do with blowing up police cars. That would presumably be covered by a reasonable force standard. The magistrates would make an argument, I imagine, that mutants and, especially, escaped mutates are so dangerous to the Genoshan state that uses of force that would otherwise be per se unreasonable (blowing up police cars and shooting NYPD officers, for instance) becomes reasonable.

Of course, international law comes in here, too, since we have authorities chasing fugitives into a foreign country. To get away with that, you need either a treaty allowing it, or the fugitives to have been engaged in a crime against humanity generally, rather than one nation individually. Piracy is the classic example.

It’s hard to see how a pursuit under whatever the Genoshan equivalent of the Fugitive Slave Act is would qualify, so the United States must have a treaty with Genosha re: the return of escaped mutates.