Apparently on August 21, 2011, NASA put together a report titled "Would Contact with Extraterrestrials Benefit or Harm Humanity? A Scenario Analysis." that answers just that. Also found on Amazon for 1.99. This doesn't cover how a country would respond but how NASA would handle several scenarios to the idea. I'm guessing since NASA is heavily funded by the United States and this document was published, the United States would obviously have regulations with NASA in mind if this were to occur.
In the first contact scenario, NASA specifies that we should train our minds in the case that we become in contact with ETI (Extraterrestrial intelligence) so that "our minds grow accustomed to thinking about, identifying and analyzing specific scenarios and variations of them". They believe that by training our minds we will have a better capacity to analyze and respond to ETI contact. They break these scenarios into two parts: intentionally or unintentionally harmful, which personally seems very science-fiction.
Being that this is a scientific paper, I found it very inspiring that they talked about handling communication. Since our common form of communication is through specific wavelengths it's impossible to know if we could ever be able to communicate with them. If an ETI is transmitting on an uncommon communication method, it's unknown how we could communicate.
The possibility also remains that ETI do not use electromagnetic
radiation for communication but instead have discovered some other
method (possibly something more efficient or effective) for exchanging
information across astronomical distances.
Also, it is noted that communication over vast distances might limit the ability for ETI to engage in warfare. Thus, even if we do discover ETI, the time it takes to communicate could be hundreds of years due to sheer distance.
This difficulty in communicating across such vast distances also might
limit the ability for ETI to engage in interstellar warfare for the
simple reason that the communications problem renders such warfare too
logistically difficult to coordinate.
which starts the next interesting subject of
"Another implication of these long communication times across the
galaxy is that ETI might become alerted to our presence without us
Once ETI become alerted to our presence, it will take at least as many
years for us to realize that they know we are here. During the
intervening time, ETI can respond to our presence or prepare for
contact in ways that we would have no knowledge of or influence on.
Even if humanity can successfully exchange signals with ETI, there is
no guarantee that the information will be successfully communicated.
In order for information to be exchanged, it is also necessary that
humans and ETI understand the contents of each others’ messages.
The answer to the concern with communication is that we would obviously communicate through mathematical conversation. Which is hinted to be our first few exchanges with ETI. They also talk about increasing the framework with METI to increase the probability of communication any time a transmission is sent from earth.
In the same section of communication this paragraph stood out to me:
For example, we are almost guaranteed to lose in a fight between us
and them, and there is a strong likelihood that such a loss would be
so severe that we would cease to survive as a civilization. On the
other hand, if ETI decide to use their superior abilities to help us,
then they may be able to help solve many of our problems.
It's obvious that depending on the situation how we handle a discovery depends on the nature of the ETI. I find it kind of sad that throughout this document that it's a worry that ETI will be harmful to civilization. You would think that if we are searching and they are searching for life outside of their own, we would be peaceful not looking to destroy one another due to fear. In any case, if the ETI are war-minded and more advanced, the odds of survival are small, so we are prepared to lose, but if they come with open-arms, we are ready to work together to "solve many of our problems". It would be pretty awesome to have ETIs come to us with cures to our diseases.
I don't think people are interested in my analysis of the paper but I just wanted to give you a bit of an introduction of what's inside. I haven't read the entire thing yet and what I have covered has only been 8 pages in. NASA obviously has interest in how we should respond. They even go into the topics of Extraterrestrial ethics: Selfishness and universalism, Possible ETI heterogeneity, benefits, handling mere detection, how we would cooperate, and so much more. I am really excited to read the entire article.
Great question again, I am glad I took the time to answer this. After I read it and find more interesting information, I am going to post more information on this topic on my personal website. Mainly because I don't want to get an award for the longest answer on a Stack Exchange site. :D