Fred, actually crows don't migrate anyplace, but their federal classification is that of a migratory bird. I know at one point there was a federal prohibition against keeping them as pets. I haven't kept up on that stuff, so maybe it no longer exists.
I did several graduate research projects on crows and jays, and as I said, I have had quite a bit of experience with them in captivity.
Just bear in mind how long lived they are. Having one in captivity is more than a lifelong committment, because it would be almost impossible to successfully release a crow that had been raised as a pet, into the wild. So, you or your descendents would be in charge of an extremely intelligent and mischievious creature. And let me tell you that crows are capable of all kinds of mischief. With the combination of extreme intelligence, flight and the extreme dexterity of their beaks, they would not be an easy pet to keep. Believe it or not they have great curiosity in all things that are shiny and things that make interesting sounds. They love to steal and hide shiney objects (one once stole and hid my car keys), and if they can't lift it, they try to take it apart. You would not believe what they are capable of dismantling. One of my flightless captive crows, could take apart small bells, and then put them together again. They could easily wreck havoc in a house. They're also too large and intelligent to be kept in cages. They're social, and need constant contact with their family, which would be you. You have no idea how loud a crow is inside a house.
So...I would strongly reccommend against a pet crow!!! It wouldn't be fair to you or the crow!!! They are not well suited to captivity.