Public figures, such as politicians, who often talk to the press, sometimes answer "No comment," meaning they are not going to answer the question. It is sometimes an unfriendly answer to a unfriendly question.
For example:
Reporter: "Have you come to an agreement in the negotiations?"
Politician: "No comment."
"No comment" is not a complete English sentence, and therefore it is not, strictly, grammatically correct. It is a short version of "I have no comment on that."
I believe the reason why the singular, "comment" is used, is because the context is an answer to a single question.