Given your few facts, I can only answer in general terms. Yes the police can run random checks, so long as they are random. In essence, they cannot select a car based on the driver, but they can run every 3rd, 5th, etc car. Good luck.
DISCLAIMER I do not practice law in your State. This answer is provided solely for informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.