I want to put some Phoenix Wright music onto a video I'm making, but what do I do in terms of copyright? Do I just give credit to Capcom (or whoever did the music) in the video, do I have to notify Capcom myself, or do I do something else? Help would be much appreciated.

Never really thought in depth about it; I typically just stick credits in the video if I'm using Capcom music (or in my case, covering Capcom music). I think it's okay to do that, just something to let the world know that you aren't taking credit for the actual song. And if it's not okay... well, to be honest, I've never had to find out if it wasn't.

You could try to notify Capcom yourself, if you really wanted to, but you might be waiting one heck of a long time for a response.

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...and the response could be a "cease and desist" order <_<

Just give credit, make sure that you make clear it's not yours, and make sure whatever you're doing it in isn't for profit.

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