We need to know what the title certificate shows as to the owner of the car. If your mother is the only named owner, the answer to your question is easier, but if another person's name is also on the title, that changes things. Also, have you been appointed as executor of your mother's estate? By this I mean, has a court in the county where your mother lived appointed you as the executor of her estate - issued you a paper called "Letters of Office"? IF your the title shows only your mother as the owner and IF you have the letters of office issued by the probate court in which your mother lived, then you can sign the title. If you have been appointed executor, I assume you already have an Illinois lawyer.
If you have no letters of office, and if your mother's whole estate is valued at less than $100,000, and if you are entitled to the car, either under the terms of her will or otherwise, you may still be able to sign the title, providing along with the title what is called a "Small Estate Affidavit." The Illinois Legal Aid Society has a good article on using the Small Estate Affidavit which I am linking below, and the State Treasurer has a fillable Small Estate Affidavit form which I am also linking below.
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