Renter's insurance is a product purchase by a lessor to protect against loss of their personal belongings in a house they do not own, but are paying rent for. Renter's insurance also includes $300,000 of liability coverage should the tenant be found legally liable for any damages to the property they are paying rent for. This type of insurance is not deductible on any tax return - be it state or federal.
I suspect you may be confusing this with the "renters credit". Some states that tax personal income will allow those who pay rent for their primary residence to claim a renter's credit on their state return. It's basically allowing them to deduct a portion of the rent they paid, as a credit or deduction for the property taxes paid by the owner out of the rental income.
