Can I refuse to sign a nursing home contract as the responsible party? I signed the contract under resident signature as her POA.

Yes you can refuse. Tell them ur only signing as her POA which does not make u personally responsible. As her POA ur guaranteeing the money is there for her care.

You have signed correctly legally. NEVER sign as the responsible party. You sign as POA and you ARE responsible to pay out of her funds. If problems continue you are paid out of POA to see an attorney for legal help.