Yes you can refuse to accept certified mail.
If you refuse to accept the certified mail then the certified mail will just be sent back to the person or place who sent it to you.
However if it's a letter about a legal matter then it's best to sign for it because refusing the certified letter may cause a judge to decide in the other persons favor.
That is if it's a legal letter that someone sent for suing you or requiring you to go to court.
A certified letter is not always bad news but most commonly certified letters are sent when something is bad news but not always.
Certified Letters are not always bad news.
However sometimes a summons, city letter etc can be sent through certified mail.
But just because you get a certified letter it does not mean that anything bad is happening is gonna happen.
Some people send certified letters when they want to ensure you get it.
I've had a friend who was trying to contact me and sent me a certified letter to ensure I got it.
But I've also had court summons, city code enforcement letters etc sent by certified mail.
If it is a legal document being sent by certified mail it's best you accept it as refusal to accept a certified letter can result in the Judge deciding against you.
But you don't have to legally sign for a certified letter if you do not want too.
Sending a letter through certified mail costs at around $6.50 per certified mail piece.
Some places may be a bit higher and some may be a bit lower but whenever I had to send a certified letter from my local post office it cost me $6.50
There's no guarantee that you'll get the letter to the recipient though even through certified mail.
But if someone does get the letter the addressee must be the one that signs for the certified letter to get it to them.
If no one signs for the certified letter then it will be sent back to you at no additional charge.