The movie scared me silly when I was a kid, but then I lived in a desert with lots of big rocks. The special effects were actually very effective for B movies. I got a copy of it on VHS just for the nostalgia.
The town was called San Angelo. An elderly Professor Flanders brought up possible scientific explanations. Ginny Simpson was a little girl who brought one of the rocks home, washed it off in some water, which grew into a huge black crystal that crushed her family home, she survived, but her hand was "petrified".
The idea was that the rocks were able to draw silicon out of living materials and sand, but needed water to activate the reaction. People became "petrified" because they lost the elasticity from the silicon in their bodies.