There should not be a problem with accepting the gift of a car. The bankruptcy estate is established as of the date of filing. If you were buying the car yourself and had a significant downpayment that was not exempted on your petition then that might lead to questions from the trustee. I am only licensed in MN and WI so you should check with your bankruptcy attorney to confirm that the MI trustees do not view this differently.
Any property that you receive within 180 days after you filed your bankruptcy becomes part of the bankruptcy estate. This means you would need to amend your bankruptcy schedules to show the new asset. There is a possibility that the Trustee could attempt to sell the asset and use it to pay creditors. If the car is not valuable, or if you still have exemptions available, it should not be too much of an issue. However, your duty as a debtor while still in bankruptcy is to update the Court to any changes of circumstances, including you getting a new vehicle.
You also need to consider your liability with regard to putting a friend's car in your name. Your question does not indicate why the friend wants to transfer the title. If it's because you have been driving the car, and they just want to make the transfer official, then it is less of a problem. If your friend is still driving the vehicle, you need to be concerned about insurance and your liability as the owner of the vehicle, should the car be involved in an accident.
I cannot tell you what to do, but the above outlines some of the risks and responsibilities involved if you choose to put the vehicle in your name.
Ms. Novak's analysis is correct. The automobile does not become an asset of the bankruptcy estate. If there is no reason to believe that the car was actually owned by you as of the date of the bankruptcy petition or that your receipt of title does not evidence an asset which existed as of the date of the bankruptcy petition, your receipt of title to the car should be considered to be part of your "fresh start".
The 180-day rule referred to by the other attorney who responded applies to certain other types of property, such as inherited property and life-insurance proceeds. Unless the car represents that type of property, the 180-day rule is not relevant.
One other point. Mr. Beuchler raised good questions about the reason why your friend wants to put a car title in your name. Under Michigan law, automobile ownership entails potential liability. And if your friend is attempting to avoid his or her creditors, you should question whether you want to get involved in a transaction which could drag you into a lawsuit.