Sounds like a critter of some sort--my guess would be squirrel/s. Personally, I wouldn't call an exterminator; I wouldn't want the dead body stinking. I'd call AC for ideas; some ACs will loan traps to residents, or they may be able to rec. a local critter catcher.

PS--I don't think it would be bats, because they can fly and shouldn't need to scuffle around.