After watching the enjoyable remake starring giant handed Chloe Moretz, I started to think after the inquiry at the end, what crime could they prove Carrie carried out? Telekinesis could not be used as evidence could it!?
Well they wouldn't necessarily have to believe Carrie had 'Telekinesis' in order to carry out the murders.
The purpose of the following investigation would almost certainly be attempting to rule that out, unequivocally.
The people who witnessed her most supernatural feats (flying, lifting people off the ground) were mostly murdered in the school hall. Cause of Death: Fire/Being Trampled (trauma)/impaled by various falling debris.
As for the remaining witnesses, Hysteria has been attributed to mass hallucination on other occasions in the past.
The Punch was rumored to be spiked with Alcohol, so what else could have been said to be in there? Remember Ms. Desjardin, one of the only surviving witnesses, distinctly hears this comment being made.
There were no witnesses (we know of) to the murder of Tina, that could have been simply a crash into a Gas Station caused by the damaged road surface.
The fact that huge chunks of the road were shattered and cracked, not to mention building collapse would perhaps point to tectonic activity.
Officials would probably assume mass hysteria coupled with a co-incidental earthquake or other seismic event which tore most of the town up.
That being said, however, there is obviously a lot of accusation being publicly leveled at Carrie, given the graffiti on her Gravestone.
The Authorities, as you've pointed out, couldn't necessarily pin anything on her. Not because she isn't guilty, but because admitting she perpetrated murder through 'Telekinetic' means is a conclusion they would be purposefully trying to evade.
As you've no doubt recognized yourself, its not possible to accuse someone (even posthumously) of murder unless you have clear and concise evidence proving their guilt through tangible means.