If it's so similar that people might get confused and think your product is from the other company, it could violate trademark law. 15 U.S. Code § 1125 says in part:
Any person who, on or in connection with any goods or services, or any container for goods, uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which—
(A) is likely to cause confusion, or to cause mistake, or to deceive as to the affiliation, connection, or association of such person with another person, or as to the origin, sponsorship, or approval of his or her goods, services, or commercial activities by another person...
shall be liable in a civil action by any person who believes that he or she is or is likely to be damaged by such act.
It's also possible that copyright could come into play, depending on the level of creativity involved.