I've spent some time working visiting a lot of websites and typing in "crayfish" in an attempt to find laws that might be relevant to people who are interested in keeping Marmorkrebs as research subjects or pets. Here's a short summary of what I've found so far.
States regulating import or sale of crayfish: Arizona, California, Minnesota, Utah
States prohibiting release of crayfish into local waters: Alabama, Arkansas, Florida. It goes without saying that pets should never, ever be released into the wild regardless of whether a local law prohibits it or not.
I'm not done searching websites yet, but I've put what I have so far here.
Update: Utah added to the list regulating import on 4 April 2009.