Is it possible to have perfect pitch but at the same time u are tone deaf?

Tone deaf would mean you can't hear the tones, perfect pitch is being able to reproduce the tones in perfect pitch (opposite of what you described). I'm really not sure it's possible to have perfect pitch (meaning you can produce the tones perfectly) but be tone deaf (not able to hear the tones). I think the opposite is more likely, where you can hear and identify the tones but are unable to vocally reproduce them (perfect pitch). My oldest daughter is kind of like that. She can hear the tones but just can't sing them. She's a great musician and violist though and is actually majoring in viola performance, just can't carry a tune in a bucket vocally, so to speak, but she can hear a song and sit down and play it on the piano or viola no problem.