It is not illegal to refuse certified mail.
Certified mail is just mail that has been sent to you with a signature required to receive it so that the sender of the certified mail can have proof that you got the mail they sent.
There's no legal requirement to accept certified mail or sign for it.
You can either let the post office or postal worker know that you're refusing the certified mail and they will return it to the sender.
Even if the certified mail is from a court, legal system, attorney, city etc you are never required by law to sign for the certified mail.
I'm actually dealing with this same thing myself in small town where they are trying to enact ordinances that have not been there for 37 years.
I own a property in that town and got a certified letter from them 3 months ago and refused to sign it and later they sent me a non certified letter demanding I get my grass mowed or I would be in court.
And they said that I had refused to sign the certified letter they sent and that it was illegal to refuse it so they issued me a court citation which in that town is not even enforceable because they have not actual police department or any contract with a police department.
I discussed it with the county police that takes care of the county and that town and they said it was not enforceable and they could not enforce any ordinances.
They sent me another certified letter 3 months later and I refused it again and will continue to refuse it.
I will have someone mow it anyway but not because they say so.
Either way not not signing for certified mail is in no way illegal and you have every right to do so.
Although if the certified mail is a court summons from an actual legal court and you refuse then you could get into trouble and have a warrant for your arrest.
So if the certified mail seems very important or comes from a legal court system where you must appear in court then it's best to sign for it.
But other than that, if it's other certified mail you can refuse to sign for it.