Looks good. I think this is a useful refactoring. There is a more general, less useful refactor that adds a type annotation on any declaration that could have one, but doesn't need to. I don't think this PR should add that (1) because it's less useful (2) I can't remember how to make a single refactoring produce multiple fixes -- it may not be possible.

@jessetrinity can you take a look too? What is your opinion on the more general refactoring?

Perhaps there should be some tests with multiple signatures:

// bad code - there should still be a test so that we at least know what the refactor does in this case, if doing nothing is too complicated.
function f(x: number) {
    return 1;
}
function f(x: number) {
    return "1";
}

// good code (?) - grabbing the first signature will add "number" as the return type, but we probably wanted "number | string"
function f(x: number): number;
function f(x: string): string;
function f(x: string | number) {
  return typeof(x) === "string" ? "a" : 1;
}