I don't think so, she has never mentioned it, even in autobiographies and other articles.
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I don't think it was ever brought up, but at the beginning Andy talks of losing his wife (Opie's mom), which why Aunt Bea lives with them.
Yes, Andy is probably the gayest thing you'd ever see, even if you don't see him he is still the gayest thing ever.
If this was the title character, certainly, a Police-type garrison hat, as officers customarily wear even indoors, like the Pentagon.