If auto insurance is required for home health job and I have to show them proof of insurance each renewal Is this auto insurance deductible?

I presume that you have to drive your personal vehicle in the course of your work.    In that case, if you claim the standard mileage deduction, the standard amount includes allowances for insurance, as well as fuel, maintenance and repairs.   If you choose to use the actual expense method, then insurance is one of the allowable expenses.   

To deduct your mileage using the standard method, you must have accurate records, such as a diary or logbook, showing the date of travel, the business purpose of the travel, and the number of miles driven.    To use the actual expense method, you need the same mileage records, plus your total vehicle miles for the year, plus records and receipts for all of your expenses, such as insurance, fuel, repairs and maintenance, and depreciation. Then, you deduct the percentage of your total expenses that is the percentage of business use of the vehicle.  For most people, the standard mileage method is easier to use and results in a larger deduction. 

Important! Starting in 2018, the recent tax law eliminates  the deduction for unreimbursed job expenses for W-2 employees.    You may want to discuss a new arrangement with your employer if you are to continue to use your personal vehicle for business.