I was reading Janet Evanovich’s “Three To Get Deadly” and Jackie the hooker hires Stephanie to find her boyfriend/pimp who ran off with her car.
They find the Jackie’s boyfriend/pimp but he’s already dead. Jackie gets upset not because he’s dead but because she wanted to kill him for stealing her car. So she pulls out a gun and shoots the corpse.
Stephanie says “I think it’s agains the law to shoot a dead person?”
Is it???
Sounds like desecration of a corpse, to me. That’d be a crime, though not one as serious as shooting a live person, of course.
Any reason you seem so desperate to make sure? 
Generally, yes, desecration of a corpse is illegal. Here it’s called “abuse of corpse,” a class A misdemeanor. One of the defense lawyers in the Manson family trials argued that his client (one of the women, I forget which) had only stabbed an already dead body and was guilty of nothing more than desecration.
It is also legal to shoot road kill deer out of season.
And, as we learned in the news recently, it’s not bestiality to have sex with a dead horse.
I hesitantly ask for a link to that last reference to the news
If Law & Order (a reliable source for legal questions if ever there was one) is to be believed, this is a variation on an old law school hypothetical. Person A sees Person B on a couch. Believing Person B to be sleeping, Person A shoots Person B in the head. However, Person B has suffered a massive heart attack and is already dead. Is Person A guilty of murder? IIRC Person A is not guilty of murder but is guilty of attempted murder. At least in Law & Orderville.
It is, however, a terrible social faux pas to beat one.
I asked a related question a while back…
Can you murder a corpse?