TITLE 18 > PART I > CHAPTER 43 > § 912

§ 912. Officer or employee of the United States

Whoever falsely assumes or pretends to be an officer or employee acting under the authority of the United States or any department, agency or officer thereof, and acts as such, or in such pretended character demands or obtains any money, paper, document, or thing of value, shall be fined under this title or imprisoned not more than three years, or both.

From US Code. Most state laws are similar. The operative thing that makes it illegal is impersonating for the purpose of getting something, other than just a reaction, that you couldn't otherwise get. When someone calls my phone, I'm free to answer it any way I choose to, even "8th precinct, Detective Jones speaking." That's not impersonating, by a legal definition. I could not legally put on a uniform, knock on someone's door, and say "I need to search your house."

Of course, to avoid any possibility of such implications, when a telemarketer calls, you could always just say something like, "mmm, you have a sexy voice, I'm going to stroke my cock while you talk..."