In Ohio, and many states, the answer to that question is probably yes. We get a lot of calls from employees who have been working at a job for a period of time, then their employer comes to them with a non-compete agreement and wants them to sign it.
Generally, an employer can require an employee to sign a non-compete agreement, even in the middle of their employment. If that happens to you, you need to carefully consider whether you want to be bound by that non-compete agreement.
The only way to really know that is to consult with an experienced employment lawyer who can review the contract, who can talk to you about the situation and give you some advice about whether or not that employment agreement is enforceable, how it might affect your future job prospects, and help you decide whether it’s more important to keep your current job by signing the non-compete, or whether to keep your options open by not signing a non-compete.