What is Ohio's state vegetable?

It's the tomato. Reynoldsburg, Ohio claims to be the birthplace of the tomato.

https://en.wikipedia.org/wiki/Reynoldsburg,_Ohio

[Added link for Reynoldsburg, it does not contain any reference to a state vegetable. - McG]

Beg to differ - but Ohio does not have an "official" vegetable. Tomato juice is the official drink - see below.

5.08. Official State beverage. The canned, processed juice and pulp of the fruit of the herb Lycopersicon esculentum, commonly known as tomato juice, is hereby adopted as the official beverage of the state.
History 131 v 5. Eff 10-6-65

https://statesymbolsusa.org/symbol-official-item/ohio/state-food-agriculture-symbol/tomato-juice