Can Texas police pull over a parked car?

I'm not sure how anyone could "pull over" a car that was parked. Police can investigate a parked vehicle that is parked unlawfully or that appears suspicious. If the car is in a public place, an officer would not require any probable cause to look at it more closely than he could by just driving by. If the car is occupied, he can ask to speak to the occupants. The occupants don't necessarily have to talk with him.

Parenthetical Comment: As an F.Y.I. - - even if the car is 'parked' - if it is occupied and someone is sitting behind the wheel, then that person is deemed to be "in control" of the vehicle whether or not it is moving or the engine is running.