|Male Red-breasted nuthatch.|
One can tell most bird species' sex by its plumage--females tend to have vastly different plumage, usually drab to help them blend in while on the nest. There are exceptions, of course, like Blue jays, where both the male and female share color and markings. In other species the difference are subtle, and easily missed if you're not really paying attention, or don't know what to look for.
Nuthatches fall into the latter group. It was only recently that I learned how to tell male and female White-breasted nuthatches apart--the male had a black cap, while the female's is gray. While I watched an RBN the other day I wondered if the same applied to the male and female of that species, and indeed it does.
Overall the male red-breasted is more brightly marked--black on top of the head, brighter sides/belly, and more blue on its back.
Silly face--birds look so odd when seen straight on.
Classic nuthatch pose.
The female shares the male's coloration and markings, but is overall duller in color, with a gray cap, pale sides/belly and more brown on her back and wings. Both have that distinctive black eye line.
Compare her to the male, shown again below.
Here's a better look at her back and cap.