It's the Copyright Bugbear again
According to UK copyright law, Casablanca is still under copyright until 70 years after the death of the author - which is ridiculous, and makes the copyright term really hard to calculate.
In US copyright law, the case is clearer - the film is covered by copyright, and can only be shown with permission and appropriate royalties paid to the copyright owner.
But in New Zealand, for one country, copyright in a movie expires 50 years after it's first shown to the public, so it seems likely that Casablanca (being 70 years old) has been out of copyright for a while, and anyone who could be bothered could freely broadcast it, burn it to DVDs and rent or sell them, or distribute in any other way they see fit.
Oddly enough, though, they don't.