Although a resolution is not required for personal car use for business purposes, it is recommended. Personal car use for business purposes can have beneficial tax implications for you as a business owner, proper documentation and record keeping of this use is important when asking for IRS deductions.
If a personal car is used for business in a corporation with directors and shareholders, it is important to disclose the information and get approval with all decision makers. A resolution may be needed in this case to document the approval and subsequent tax deduction or mile reimbursement requests.