Absolutely not. This is a common scam used by fraudsters to steal your banking information.
For example, here is how one scam works. A scammer sends you a check for more than the agreed upon amount. They then ask you to send a check back for the overpayment. When you do, they get the name of your bank, your account number, and a copy of your signature.
No legitimate person will ever send you a check without doing some serious due diligence.