WASHINGTON — The Supreme Court on Monday agreed to decide whether Secret Service agents protecting Vice President Dick Cheney may be sued for violating the free speech rights of a member of the public who made critical remarks about the Bush administration’s war policies.

The case arose from an episode in 2006 at a mall in Beaver Creek, Colo. A Secret Service agent said he heard Steven Howards say into a cellphone that he planned to ask Mr. Cheney “how many kids he’s killed today.” Mr. Howards later approached Mr. Cheney and said the administration’s “policies in Iraq are disgusting.” Mr. Howards then touched Mr. Cheney on the shoulder in a gesture variously described as an open-handed pat, a slap and a strike that caused the vice president’s shoulder to dip.

Confronted by the Secret Service, Mr. Howards denied touching Mr. Cheney and said, “If you don’t want other people sharing their opinions, you should have him avoid public places.” Agents arrested Mr. Howards for assault and turned him over to local authorities. He was charged with harassment under state law, but those charges were later dropped.

Mr. Howards sued several Secret Service agents, saying his arrest was unlawful. He said the agents had violated the Fourth Amendment, which bars unreasonable searches and seizures, by arresting him without probable cause. He added that the arrest had violated his First Amendment rights because, he said, it was made in retaliation for exercising his right to free speech.