http://www.rosen.com/divorce/divorcearticles/when-is-annulment-an-option/
This is a discussion of the question of legal annulment in North Carolina. (Each state can have different guidelines.) Some of the criteria are similar to those involved in a Church declaration of nullity, but others are not. In particular, the law says that if a couple has lived together and had a child following the marriage, there can be no annulment, except in cases of bigamy.
A weird element: in NC, the marriage can be annulled if “either party” is impotent. That almost seems to be setting up marriage for homosexual men, since “impotence” is unique to men. A woman would have to be drastically mutilated or injured for intercourse to be impossible, whether she consents to it or not.
The wording of that law may be very, very old, and a hold-over from a time when there was thought to be a medical, physical condition called “frigidity” that was roughly an analog to male impotence. Although the word is still in use, the meaning has shifted in that it's no longer a respectable opinion to think that there are women who are literally, physically frigid.
sitetest
There are women who can’t conceive, and I know of at least one marriage that ended because he wanted kids and never got any, so he left, remarried, and then had kids. Although “impotent” does connote male failure-to-perform.
An annulment in a civil sense would require some other reason like fraud, bigamy, or some such, as opposed to the acceptable reasons for divorce like, infidelity, impotence (failure to discharge marital duties), abuse, etc.
Annulment would mean that the marriage contract was invalid when made.