Do I contact my insurance company and let them know?
Yes. In fact you should have given this information at the time, as well as your name and address.
Where do I stand if I refuse to accept responsibilty?
Probably you will end up in court.
Do I contact HIS insurance company saying i am not accepting responsibility?
That's up tpo you to decide. But, as said above, you are responsible. How can you not be responsible when you were moving at the time and the other car was parked?