If by "Database" you mean the coollection file that contains your personal data
https://www.coollector.com/help.html#coollectionyes you can put it in a common folder and access it from both computers (though you won't be allowed to make changes from both simulteanously, i.e. when a computer makes changes to the coollection file, the other computer will notice and ask to reload it).
If you mean the movie database, the pictures, etc... I'm afraid it's impossible because Mac and Windows apps are using very different file locations.