The case before the court pits Local 269 of the International Brotherhood of Electrical Workers against the central Jersey town of Lawrence.
When the union used the rat in a 2005 protest at a construction site, the township slapped its business agent with a fine. It claimed the 10-foot rubber rodent violated an ordinance against balloons and other inflatable signs.
Lawyers for the union argued yesterday that the law violates their right to free expression and suppresses protest.
The township argues the union's use of the rat is a form of commercial speech, less deserving of protection than religious or political expression.
The justices didn't indicate when they would rule.