The MKR Group (owners of the copyright to George Romero's Dead films) and New Line Cinema have seen Dead Rising, and do not like what they see. Ever since the game's release, MKR and Capcom have been in discussions aimed at resolving what MKR see in Dead Rising as a premise and setting a little too close to Dawn of the Dead for their liking. It's why, for example, the game's box features the disclaimer "This game was not developed, approved or licensed by the owners or creators of George A. Romero's Dawn of the Dead".
Those discussions have gone nowhere, however, culminating in a letter from New Line - allegedly sent to Capcom, Microsoft and Best Buy - complaining that Dead Rising is just far too similar to Dawn of the Dead. This letter has sparked fears at Capcom that MKR are about to assert their copyrights and trademarks over Romero's works, will claim Dead Rising is in violation of these and take legal action. In an attempt to head this action off at the pass, Capcom's lawyers are seeking a declaratory judgement (ie a judge to say what they've done with DR is fine) and attorney's fees, and are claiming that "humans battling zombies in a shopping mall" is a "wholly unprotectible idea" under current copyright standards.
Which of course it is. It shouldn't take a court of law to decide that.
Capcom v The MKR Group Legal Documents [The Hollywood Reporter]