I don't think so, no. Her father was a police officer, and I don't think her mother ever gets mentioned. Her apartment is quite fancy, but I think that's because she's a fairly-high-level, presumably well-paid government official, not from old family money.

Rather, I think her indifference to the vast amount of cash* Joker had on him is just an artifact of the way RPGs are almost always silly about money and inventory in general. It's sort of like how there are only coins in the Elder Scrolls universe, but your character can be carrying around what would work out to a couple of tons of gold in his pockets, along with 44 weapons, three or four complete suits of armor, enough magic potions to flood a small village, and an entire wine and cheese cellar. :)

--G.
* and it must be cash, because most of it came from monster drops, and they're hardly going to stand there making bank card transfers before they die
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