Can I deduct my apartment rent that i paid, on my state income tax return?

There is not a rent deduction or credit on your Federal return.  If your state has anything for renters you will be prompted to enter your rent info when you complete your state return.  As far as I know, the states that have anything for rent are Arizona, California, Connecticut, Hawaii, Indiana, Iowa, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, New York, Rhode Island, Vermont, Washington DC, and Wisconsin.

The IRS won't let you deduct rent for your personal residence.  However, there's a deduction for home offices, and expenses related to rental property you own are deductible.

A handful of states have some type of renters' tax credit for a personal residence or apartment.   If your state is one of them, we'll ask rent-related questions when you go through your state interview.

Can I deduct rent?