If an astronaut murdered their fellow astronauts on the ISS, what exactly would happen next? And under which state’s law would their crime be prosecuted?

Buzz Lightyear would come and take care of it

Where?

I think they get voted off. Dude puts their fire out and they exit out the doors.

It wouldn’t, because it was a crime without gravity.

It’s similar to the law of the sea. The country of the criminal is expected to try them . If they fail to do so the country of the victim has the right to try them. The country who owns the space vehicle also has jurisdiction so technically you could have 3 cases to answer to.