There are a couple of things that would need clarification to best answer your question.
First of all, every state has specific requirements about specifically distributing assets after death. This is usually done via what you may know as a will. Most states require that any document (or note) leaving property to another after death be signed and witnessed (at a minimum).
Second of all, when you talk about listing the car as an asset, I am imagining that you are talking about an Administration (died without will) or Probate proceeding (died with will). The specific terms for these proceedings may vary according to your state.
While it's impossible to answer your question fully without additional information, the short answer is that absent any other controllling documents (trusts, etc.) the car would be an "asset".
You really will want to consult with a local estate attorney to iron this out.
You need to see a probate lawyer.
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I am very sorry for this loss. The answer to your question would depend on how the car is titled. The other things to remember are that a suicide note may not be a valid will, and that depending on the individual's assets, an Affidavit of TRANSFER which is what I think you are describing, may or may not not be the correct legal procedure. I strongly advise you to talk with a probate lawyer in the area where this individual was living at the time of his or her death.
I concur with the other counsel. It is difficult to tell what you are asking here. The affidavit of Transfer can be relevant when a car is left behind by a decedent. There are also forms that the Department of Motor Vehicles has that you may be able to use to transfer a car to a survivor. So much depends on unknown facts. You really should consult with an attorney that can give you the best answer after hearing your story in greater detail. Good luck to you during such a trying time.