If he did not leave a will and there is no secured interest in the vehicle it would go to his living issue..meaning it will be divided among the living children. However if his estate is probated the result may be different in accordance with his will..
Under Michigan law, as long as the vehicle is worth less than $60,000, probate is not necessary. You can complete a certificate at the Secretary of State and the vehicle would be re-titled in your name and your sister's. The girlfriend would have no interest in the vehicle, although you could certainly sell it to her, if you wish to.
I am licensed to practice law in the State of Michigan and have offices in Wayne and Ingham Counties. My practice is focused in the areas of estate planning and probate administration. I am ethically required to state that the above answer does not create an attorney/client relationship. These responses should be considered general legal education and are intended to provide general information about the question asked. Frequently, the question does not include important facts that, if known, could significantly change the answer. Information provided on this site should not be used as a substitute for competent legal advice from a licensed attorney that practices in the subject area in your state. The law changes frequently and varies from state to state.
Assuming there is no will, the vehicle passes to you and your sister, in equal shares. The vehicle can be sold or the two of you can work something out so one gets the vehicle and the other gets some cash. If you keep the car, you must get insurance. Notifying the insurance company of your father's death may result if a partial refund of the premium for the insurance in force at the time of his death.
You should not rely on this answer. You should consult a lawyer so you can tell the lawyer the entire situation and get legal advice that is precisely tailored to your case.