Am I responsible for my mother's final expenses?

My mother just recently passed away from an over dose. She lives in California and I'm in Oklahoma. I did not have the money to fly out there and also had no money for her burial or whatever. The hospital told me the state would take care of it. I've received a call from the Coroner saying I would have to apply for assistance and that since I worked and owned my house I probably wouldn't qualify. I'm barely making ends meet with my own bills and already have a garnishment on my check. Can I be stuck with these bills and hospital bills too? I told her I didn't even know if I could legally be considered next of kin now because I was adopted by my grandparents (my father's parents) almost 20 years ago. My birth certificate has been changed and doesn't even show my mom's name now. I hate to be like that, I loved my mom and wish I could have been able to afford a funeral or cremation but I can't. I'm doing good to keep my dang house. She said they would go ahead and take care of it and wouldn't make me pay but she was sending me paperwork to fill out. I'm afraid to put my name on anything because I don't want to be held responsible. Can they legally come after me for this?