What can be done to someone in Tn that files a false report in SC?

If South Carolina wishes to prosecute the suspect, they can issue a warrant for his or her arrest.

At some point, police officers in Tennessee would discover that the suspect has a warrant, and they would make an arrest based on that warrant. Tennessee would then have the option to extradite the suspect from Tennessee to South Carolina, where the suspect would be charged and potentially convicted of the crime.