In the state of Texas, you are able to sell a car without registering it, as long as the car is still registered in the previous owner's name. The only time you would need to register the car in your name would be if you were planning on keeping the car for yourself. If you are selling the car to someone else, you will need to provide them with the car's registration and proof of insurance. The buyer will then be responsible for registering the car in their own name and transferring the title.