Recently I paid a lot (almost one month of my salary) for repairing my car. I am wondering if there is a way to get deduction on federal or state taxes (USA, California).
Unless you own a business and the car is used in that business you can't write off your auto repairs.
If you start a sole-proprietorship in your own name there are all sorts of things you can write off as long as there is a reasonable expectation of profit. This includes a portion of your car repairs, a portion of your home expenses (assuming it's a home-based business), any tools used in the business, all kinds of stuff. The portion of your auto is based on total miles driven in the year vs. total miles driven for business purposes. Eligible auto expenses include repairs, gas/oil, insurance, parking, and interest on the auto loan.
There are some things to remember:
I'm no expert on California business law. Talk to a lawyer and an accountant if you wish to go this way. Many offer a half-hour free session for new clients.