Back in March, Ohio passed statewide preemption of all local gun laws (except for zoning regs and discharge of firearm in city limits, etc.) so any local ordinances relating to magazine capacity are history. (Although Cleveland is being its normal big filthy babyish self and trying to fight this. But I digress).
The only state restriction would be on magazines of over 30-31* round capacity. In short it's legal to buy, sell, or possess them, they become illegal when you put them together with the firearm they're made for.
But it's a rarely enforced, little known statute. Many stores in Ohio sell 40+ round mags for ARs, AKs, etc. on a regular basis, in fact I'm told they're even available at the National Matches going on at Camp Perry. And, going by the word of prosecutors I've known over 25 years of competition, no one has ever been charged with violating just this law, it seems to be used only when "piling on" charges against someone accused of multiple serious crimes.
*The wording of the law in question is so strange, it's hard to figure out what the "magic number" really is. In fact it once used to read "over 36 rounds" as memory serves.
Hope all this helps.
"Rex, you shot him in the head!---How do you feel about that?" --'Rustler's Rhapsody'