re: Who's the boss, city cops, state cops, or the Feds? (death penalty enquiry)

Quote from the subject ‘Who’s the boss, city cops, state cops, or the Feds?’
“As a practical matter, though, all local and federal agencies subscribe to the notion of “comity of jurisdictions,” meaning they try to cooperate. Normally you’ll be turned over to the authority that’s after you for the most serious offense.”

I am very curious about this statement; if someone were to commit a straightforward murder in a state which carries the death penalty, AND THEN carry on to commit a kidnap/murder (a presumably more serious crime) in another state which does not carry the death penalty. Does it mean that the murderer will be tried and sentenced in the more lenient state, thus getting away with the death penalty?

Sorry about the double post! It was an accident!