The United States Postal Service (USPS)" Domestic Mail Manual" (DMM) outlines in Section 508 how certified mail is handled. Your signature is required before the mail is considered "delivered."
Refusing Certified Mail
Before refusing certified mail, you should inspect it while the carrier or clerk still has it. The mail is not considered refused until the carrier or clerk actually presents it to you in person. Otherwise, it may be considered undeliverable-as-addressed following a notification process.
Read More: Certified Mail Requirements
Involving Legal Proceedings
Although it is not illegal to refuse certified mail, it can count against you (as the recipient) because the sender may be forced to hire process servers to complete the task and they may recoup their fees from you following a court order.
Consequences
If a moving party can provide proof of attempting to serve an individual with notices and motions via certified mail (marked "Refused"), then a court may pass judgment in favor of the sender because he has tried all he could to bring all parties to court for a hearing. This process varies from state to state.