Our employer will not allow her employees to clock themselves in or out. Only the receptionist is allowed to clock employees in or out. Is this legal in Ohio?

It may be poor management, but this is not even addressed in Ohio law. So, short of a regulation prohibiting it, it is legal.

Having said that, I would be very careful that your time card is reflecting the proper hours and that you are getting paid for all the time you work. If it were me, I would probably address my concern, politely, with HR and see what they say.