I am in the state of North Carolina. I was wondering if there is a legal way to have extra marital relations if the spouse refuses sex for a certain period of time. It has been about 1 year.
A spouse's refusal to provide sexual relations does not excuse the extra marital relations of the other.
Extra marital relations can be considered adultery and in NC adultery is a crime. I have never seen or even heard of it being prosecuted in recent years because almost everyone has violated this law at some point but it is still a valid law. § 14-184 Fornication and Adultery: If any man and woman, not being married to each other, shall lewdly and lasciviously associate, bed and cohabit together, they shall be guilty of a Class 2 Misdemeanor.
The only way I can think of to 'legally' have extra marital relations is to enter into a Separation Agreement. Most Separation Agreements have clauses that allow the parties to date and associate with whom ever they want. Since you would technically still be married any sexual relationship outside of your spouse would be extra marital.
However, while the Separation Agreement would most likely protect you and any extra marital partner(s) from civil liability you may still be violating the criminal law. I guess just try and make sure your extra marital relationships are not lewd and lascivious.