Mine crow pretty much anytime they feel like it between first light and twilight.
I have noticed something about the odd crows in the middle of the night though, everytime one of my roosters crows at night and I've gone out to check on them with my high powered flashlight, I've found an animal passing close by.
Sometimes its just a cat, dog, or a deer, and sometimes its a coyote, coon or possum, but 100 percent of the time that this has happened since I started paying attention to it there has been an animal close by.
I have to wonder if they are sending up a warning.