Great summary of the rules for personal use of a ministry vehicle here, written by Kathy Hostetler, CPA, on the Nonprofit GPS blog.
This most often becomes an issue when the ministry buys a car and lets a senior person use it as their personal vehicle. That creates taxable income. Remember that if income is not reported, the IRS could take the position the unreported amount is an automatic excess benefit, which could create a severe penalty. But that is a topic for another day.
Check out the article for a survey of the taxability rules.