My girlfriend's mother was Ghanaian, her British father died about 15 years ago. She is 36 and lives in the USA. Is she entitled to a British passport because of her father?
Your question is really about British citizenship because someone can only get a British passport if they are already a British citizen or other British national.
You didn't give enough details to determine whether she is currently a British citizen. I can give some situations in which she would be a British citizen from birth.
If she was born in the UK, she is a British citizen.
If she was born outside the UK, and her father was a British citizen at the time she was born, and specifically he was a British citizen "otherwise than by descent" (meaning he was not himself born abroad and got citizenship from a parent; if he was born in the UK or naturalized in the UK then that would be okay), she is a British citizen.
legitimate descent from a CUKC father for children born elsewhere. Only the first generation acquired British nationality automatically. Second and subsequent generations could do so only if born outside the Commonwealth (or Ireland) and registered within 12 months of birth or if the father was in Crown Service.
I agree with the previous answer. Firstly, you need to be a British Citizen in order to be eligible for a British Passport.
In case, your girlfriend doesn't have British citizenship then she will have to apply for a Certificate of Naturalisation which has specific eligibility criteria to fulfill like - must communicate in English, must be of good character and others.