If I am fixing my car and it falls on top of me will my car insurance cover it?

If this is a distinct possibility, I think you should use a car-repair shop.

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Your car insurance policy likely won't cover your injuries, because you weren't driving the car at the time.

Let's do the math: Even if you have good health insurance, your deductibles and co-insurance from your hospitalization will likely far outweigh the cost of professional car repair.