You say you are  "receiving a refund" from taxes paid to OH State.  Did you mean to say you are "receiving a credit" from NYS?

If so, yes, the NY credit includes both the state and local tax paid to another jurisdiction.  So, if you're not asked to enter the local taxed paid, separately, add boxes 17 & 19 together for this entry. 

Resident Credit

Who is eligible? 

You are entitled to claim this nonrefundable credit for the tax year if:

• you were a full-year or part-year resident of New York State, or a New York State-resident estate or trust, or a part-year resident trust; and
• you had income sourced to and taxed by another state, a local government within another state, the District of Columbia, or a Canadian province (this income generally includes wages and business income, and typically excludes interest, dividends, gambling winnings, and lottery winnings).

https://www.tax.ny.gov/pit/credits/resident_credit.htm#:~:text=Resident%20partners%2C%20members%2C%2....