Usually those requests go through the state department and if the us has an extradition treaty, the extradition is handled by the country they’re residing in.

If there is none, it’s more murky and usually handled case by case. (Or just ignored.)

If we do the asshole thing and ignore all that, it’s going to be the military, not cops. (See Maduro’s “arrest”)

Generally, cops only have authority within specific jurisdictions, sheriff’s the counties they work in and cops the cities, though if there’s a justification, they can go outside that, but it’s kinda frowned on without that justification.