There is no question that Donna Lou Rayhons had severe Alzheimer’s.

In the days before being placed in a nursing home in Garner, Iowa, last year, Mrs. Rayhons, 78, could not recall her daughters’ names or how to eat a hamburger. One day, she tried to wash her hands in the toilet of a restaurant bathroom.

But another question has become the crux of an extraordinary criminal case unfolding this week in an Iowa courtroom: Was Mrs. Rayhons able to consent to sex with her husband?

Henry Rayhons, 78, has been charged with third-degree felony sexual abuse, accused of having sex with his wife in a nursing home on May 23, 2014, eight days after staff members there told him they believed she was mentally unable to agree to sex.

It is rare, possibly unprecedented, for such circumstances to prompt criminal charges. Mr. Rayhons, a nine-term Republican state legislator, decided not to seek another term after his arrest.