They would issue a bench warrant. Then any LEO in any jurisdiction could arrest and detain him. He would have to stand for extradition, but that would be a foregone conclusion.
That’s how it would work on anyone else.
If they wanted to be real jerks, they could charge him with being a fugitive.
And…he would forfeit his bail.
Until the 1980’s state governors had broad discretion over turning over fugitives but federal law has changed and they have very little discretion now. There is however still one loophole. If the person being demanded is serving a sentence in the state he fled to the state/governor does not have to turn him over until the sentence is served. Now that leaves a lot of wiggle room if a state and governor and local court want to avail themselves of it. You “arrest” Trump, charge him with something, he pleads guilty and gets sentenced. His prison could be Mar A Lago or the governors mansion or a comfy home on the grounds of the state prison.
Would that be a smart move? Probably not, but nationally and culturally both the left and the right are ready to challenge federal supremacy, and both the left and the right have been asserting state’s rights albeit over very different issues. Sooner or later a conflict will either be ginned up or develop organically. This one would be more interesting than some of the other possibilities with echoes of the fugitive slave act to boot and we all know how that dispute evolved.