No you do not have to accept certified mail.
You can tell the USPS worker that you do not want to accept the certified mail and they will just return the certified mail to the sender.
Certified mail is not meant or able to force you to sign for or accept the certified mail.
But the certified mail is sent so that they get proof that you signed for it and to ensure you get the mail.
But you cannot be forced to accept certified mail.
When you send a certified letter through USPS you will have an official receipt showing proof the item was mailed and has been certified.
Then when the certified letter reaches the persons post office or postal box they will have to sign a form with their signature before they will get the certified letter.
So when you send a certified letter it is meant to prove that the person got the letter.
Very important documents and letters are sent certified and require the addressees signature to get the certified letter.
Then the person who sent the certified letter should receive confirmation that the certified letter was delivered to the addressee.
Certified letters cost more than a standard letter but it makes sure that the person gets it.
However nobody can be forced to sign for or take a certified letter so they could have it returned to you.
But most certified letters do get to the addressee just fine.