The headliner finishes off your car's interior by providing a finished look to your car's ceiling. Periodic care and cleaning of the headliner should be part of regular interior upkeep.

IF you have a vinyl headliner, clean it with vinyl upholstery cleaner and a soft cloth. Do not use any strong solvents or bleach. They may damage or discolor the vinyl covering. It’s also wise to avoid using abrasive cleaning pads as they can damage the vinyl surface. As you clean the headliner, use care so you’re only wiping the surface, not pushing and stretching the material. 

To clean a fabric headliner, use automotive upholstery cleaner. Never use strong chemicals or any cleaning agent that discolor or damage the fabric. Make sure to follow the instructions on the label of the cleaner for best results. To be on the safe side, it’s wise to test the color fastness of the fabric by applying the cleaner to fabric in an inconspicuous place on the headliner (in a corner or under a sun visor, for example). To combat tough stains, it may require spot pre-treatment or repeated applications.

Source carcareonline.com