I saw the Kato kid's claim that it was his family crest, but he's mistaken; after some more hunting I discovered that it belongs to the Fujiwara clan. Mon are exclusive to family names, and his reasoning for it being the Kato family arms is oblique to say the least.

Still no clue as to why it's used in a historical context in Millennium Actress, though the fact that the Fujiwara clan is historically VERY influential and powerful... which at least explains why Kato is trying to claim that it's his.

Aha! Another clue!

Later in the movie, when she's looking through the rubble of her bombed city, she sees the sign of her family's (hithero unamed) candy store: Wisteria Sweets. Her family's name isn't Fujiwara, so it's possible that Fujiwara is a placename, hence the police uniforms?

Still slightly baffling.

Still very odd that it looks so darn familiar.

According to IMDB, her character's name is Chiyoko Fujiwara. It sounds we've pieced together an answer.

Re: the Fujiwara vs. Kato thing

Fujiwara　(藤原) and Kato (加藤) both use the character 藤, which means wisteria. This site ( http://ekamon.hamazo.tv/c544623.html ) says that the maru-ni-sagari fuji (hanging wisteria in a circle) is the most common crest in Japan, and is the family crest of the Fujiwaras but is also used by many other clans that were vassals and descendents of the Fujiwaras and thus adopted the wisteria character into their own names: Kato, Saito, Ito, Kindo, etc.