No you have no obligation to go to the police station. If they just wanted to get information, I think they would come to your house. You should not speak with them witout your attorney present. If they have or get probable cause that you committed a crime they will get a warrant to arrest you regardless of whether you talk to them. Talking to them is unlikely to help you and very likely will hurt you.
I agree with Mr. Wagner. I would just add that I don't believe that the LA public defenders office will represent you prior to barging, if you want a lawyer, you will need to hire one. If you are charged and any afford an attorney, then the public defenders office will represent you.