If an employee terminates from our company before the bonus for the previous month's production has been paid, do we have a legal obligation to pay the terminated employee the bonus?

That would depend on what is in your company policies and procedures if you have any?

Most places I have knowledge of do not pay out bonuses to employees who won't be working for them next week. Bonuses are an incentive to do well. Why would you want to pay someone to do well, who's not working for you anymore?

This should be outlined in a policy and procedure manual for your business and each new employee should receive this manual.