The U.S. government does not have an official plan for what to do if we come in contact with extraterrestrial life, but an organization called the SETI (Search for Extraterrestrial Intelligence): Post-Detection Taskgroup has a set of recommendations in place.
SETI's protocol is that if anyone detects a potential radio signal from extraterrestrial life, they should get in touch with SETI researchers, who will help verify whether the signal is actually evidence of extraterrestrial intelligence. If it is, they should notify the International Astronomical Union as well as the United Nations. The discoverer would get to make the first public announcement, but data should be made available to international scientists. SETI would then determine whether a response signal is justified and what message to send if it is. This process would involve not just scientists but other experts and the government.
Many scientists believe that making contact with aliens is a very bad idea. Authors of the book Introduction to Planetary Defense: A Study of Modern Warfare Applied to Extra-Terrestrial Invasion believe humans would be like the Native Americans to the alien Europeans. They also think that our slow global response to natural disasters indicates that we could react poorly to invasion.