I am one of those types of folks who always plays a situation with the "better safe than sorry" standpoint in mind. If a car ran over your arrow then I would not being shooting it. Personal opinion.

Check very carefully around the nock end of the shaft. Alot of time when the nock pops off that means that the shaft cracked at the nock end. Also, one of the internal layers of the shaft could have cracked and yet it would not be noticeable with a visual inspection of the arrow.