You will have to check with your parish and city to see if they have any special licensing, those won't be online and most in Louisiana don't require them.
You definitely want liability insurance but you wouldn't be required to have it for mechanic's work. You would want to get a tax resale number from the state and an EIN from the IRS.
If you have employees you are required to have workers comp insurance in LA. You can read more about that at http://www.lwcc.com/
There are some job types that require a contractor's license. You would need to contact the agency at http://www.lslbc.louisiana.gov/ and ask them when it is required for your type of work. I don't think private mechanics are required to have them but private mechanics on certain type of job locations are.
That should take care of you as far as "requirements". As I said, even if you don't have to have liability insurance you probably want it and you can also talk to the same insurance company about being "bonded" sometimes that lowers the amount of liability you have to carry plus it is a good advertising point.
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