Asatani is a special investigator dispatched from Tokyo Police HQ to help crack the Cat's Eye case. She's known for being sharp and calculating—basically the Tokyo Metropolitan Police Department's idea of an elite officer. Her credentials are solid: she won the All-Japan Air Pistol Championships and holds a 4th-degree black belt in karate plus a 2nd-degree in judo, which puts her in Hitomi's league when it comes to actual combat skills.
Beyond the detective work, she's also conventionally attractive enough to have been crowned a beauty queen during one of the investigations, though that's more of a side note than anything central to her character. What matters more is that she's one of the first people to suspect Hitomi might actually be Cat's Eye—she just never manages to dig up the proof to back it up.
Her one real vulnerability is pretty mundane: she's practically helpless without her prescription glasses. It's the kind of practical weakness that actually matters in the field.
The manga hints at something the TV series largely ignores—Asatani apparently has a quiet thing for Toshio, which doesn't sit well with Hitomi. It's not a major plot point either way, but it adds an extra layer to the dynamic if you're reading between the lines.
Content compiled by AnimeList.moe from publicly available sources.