Yes. If you both used it and took a deduction for it, you would both need to enter it as you stopped using it. Even though you may be filing a joint return and are using the same vehicle, it is still treated as two separate businesses with separate use of the asset.
However, you stated that it is "my car" if you both used it but only you owned it, then she would not need to enter the sale of the vehicle on her return. She would just need to mark that she stopped using it. If the vehicle was in both of your names, then she would need to allocate her portion of the sale of the vehicle on her Schedule C.
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