Yes. These sorts of contingency plans most assuredly exist, though most of them are and will remain classified. It would be incredibly foolish and grossly incompetent of the Powers That Be if they did not have at least some rudimentary plan of action in place for them to reference quickly if the time came, however unlikely people may consider the possibility of alien visitation to be.

Military and intel agencies plan for countless possible scenarios all the time. It is a huge part of what they do - proactive thinking and planning, even if the scenario is deemed to be incredibly unlikely. There is a reason the USA has constantly updated plans to invade Canada for example, even though there is nothing at all to suggest that they would ever need to exercise that plan in the foreseeable future.

Hell, the US military even have something on the books called "CONPLAN 8888-11" (PDF warning), which is a plan to deal with a theoretical zombie invasion! Now, that might sound crazy (because it is), but many believe that the purpose to a plan like that is to use it as a training reference tool to better learn how to plan for incredibly rare and extreme scenarios, such as alien visitation/invasion.

To quote CONPLAN 8888-11 directly - "This plan fulfills fictional contingency planning guidance tasking for U.S. Strategic Command to develop a comprehensive plan to undertake military operations to preserve ‘non-zombie’ humans from the threats posed by a zombie horde. Because zombies pose a threat to all non-zombie human life, Strategic Command will be prepared to preserve the sanctity of human life and conduct operations in support of any human population — including traditional adversaries."

Just replace the word "zombie" with "alien", and you can see how this sort of contingency can be hidden in plain sight. Many people believe that CONPLAN 8888-11 (also called “Counter-Zombie Dominance,”) was actually devised as a fictional scenario that can be modified to fit a possible real-world application related to coping with a potential alien visitation/invasion. Rather than putting a plan on the open books that explicitly references "aliens", instead they substituted ET life with "zombies" in the study to allow them to play the plan off as a joke to many people who question its relevance.

As the Strategic Command puts it, "The document is identified as a training tool used in an in-house training exercise where students learn about the basic concepts of military plans and order development through a fictional training scenario". However rare the likelihood may be of an alien visitation or invasion, having at least a basic plan in place to try to deal with a potential threat that could end all life on Earth has to be taken seriously, and having a plan in place for dealing with that possibility, however remote it may be, is important. Again, it would be absurdly incompetent if a basic plan of action/response was not on the books somewhere - whether classified or public.

There are even published guidelines for emergency first responders on how to deal with something like a crashed alien spacecraft (flying saucer). The "Fire Officers Guide For Disaster Control" for example is a book found in many firehouses around the nation and is used as a reference source for firefighter training. In it, there is actually a chapter about how to deal as a first responder to a crashed spacecraft or satellite of both Earthly and extra-terrestrial origin.

Again, having some form of plan for any eventuality that could pose a serious threat to humanity, no matter how remote the odds, is just good thinking, and is not nearly as crazy as it may sound.

At the 1985 peace summit in Geneva, Ronald Reagan asked Mikhail Gorbachev for Soviet support, in case there was an imminent threat of an alien invasion from outer space. Gorbachev was taken aback by this suggestion and politely changed the subject.
General Colin Powell, who at the time was the Deputy National Security Advisor, was horrified that Reagan went off script and even brought the topic up. One of Powell's jobs as Deputy National Security Advisor was to carefully read Reagan's public speaches and delete any interplanetary references. He told Reagan that the plans the US Military had for that contingency were "Top Secret". President Reagan was only able to speak publically about an alien invasion from outer space once while president of the United States. He did so at a high school in Maryland, shortly after he returned from the 1985 Geneva summit with Gorbachev.
Source: "How UFOs Conquered the World" by David Clarke (2015)

SETI (Search for extraterrestrial intelligence) has created "Protocols for an ETI Signal Detection" which contains guidelines on how to act if humans were to discover signs of extraterrestrial life.