Major League Baseball Rule 7.05 refers to a cap. I suppose that answers the question.
7.05 Each runner including the batter-runner may, without liability to be put out,
advance—
(a) To home base, scoring a run, if a fair ball goes out of the playing field in flight and
he touched all bases legally; or if a fair ball which, in the umpire’s judgment, would
have gone out of the playing field in flight, is deflected by the act of a fielder in
throwing his glove, cap, or any article of his apparel;
(b) Three bases, if a fielder deliberately touches a fair ball with his cap, mask or any
part of his uniform detached from its proper place on his person.
baseball hat
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