I have a medical marijuana card from another state. Can I use this in your dispensary?

As of this writing, no—you cannot use an out-of-state medical marijuana card to purchase product in an Ohio dispensary.

Here is the full answer from the Ohio MMCP website:

Currently, Ohio does not recognize medical marijuana registry cards issued in other states. The law requires that the Board of Pharmacy attempt in good faith to negotiate and enter into reciprocity agreements with other states. If Ohio does enter into a reciprocity agreement with another state, more information will be posted to the OMMCP website.