If the safety didn't work on the garage door and it closed on my trunk is that home owners or a car insurance claim?

This would be an auto claim assuming that you have comprehensive coverage on your vehicle. If your car was moving at the time it would probably be a collision. Homeowners specifically excludes coverage for motorized vehicles with certain exceptions (lawnmowers, Golf carts, etc). Your claim would be subject to your auto deductible. It is not advised to make small claims so don't make a claim unless it is really worth it. I have owned a small insurance agency for the past 22 years and worked for a direct writer for 3 years before that. State laws vary somewhat but this answer should apply everywhere.