RellikWhat might have been another dreary detective chasing serial killer series is turned on its head when women portray both roles, exploring the kinds of things that aren’t often considered in such dramas.

In the stylish new “Killing Eve” (BBC America, 8 p.m.), the versatile Sandra Oh plays a frazzled, half-American desk jockey at Mi-5 who has been quietly tracking an international hitman who happens to be female, a role so unusual there isn’t really a term for it yet (hitwoman won’t do).

As the assassin, Jodie Comer (from “The White Princess”) is a tad too wide-eyed crazy. But she’s got some advice for one of her victims before she stabs him in the eye with a hairpin: Don’t touch a lady without asking first.

The mix of humor amid the tension may be thanks to the having red hot Phoebe Waller-Bridge help adapt the series from the “Vianelle” novels of Luke Jennings. Waller-Bridge was approached to help in between the time her “Fleabag” hit the stage but before it was adapted into the quite well received dark comedy series.

I read the first novella and just fell in love with these characters, just thought they were just wild, and I hadn’t seen them before and just was desperate to kind of stand them up,” Waller-Bridge said at the TV Critics Association winter press tour earlier this year. “I had not written a drama or anything like that before.”

But she said executive director Sally Woodward Gentle “thought I was mildly perverse enough.”

“We did, said Woodward Gentle. “And I realized that we had a very similar sense of humor and similar taste and similar sort of tone and attitude towards stuff. And Phoebe’s so bright. You knew that, even though you didn’t have that much experience, there was no way that you couldn’t inhabit those eight hours.”

For Oh, the “Grey’s Anatomy” star who was also in “Sideways” and “American Crime,” “I feel very much in a completely different and separate world with ‘Killing Eve.’

“I was actually really happy for the departure,” she said, and attracted to Eve’s “frazzledness, how she doesn’t have things under control … how she’s quite insecure and how she has not found her voice.”

To have the assassin and hunter “be these two female characters,” says Oh, “and also surrounded by other female characters, it’s just great to be in that world.”

“It’s women being other than wives and daughters. That’s the great pleasure,” says Fiona Shaw, who is also featured in the series. “They’re people functioning in a universe where they’re changing the world, literally. That’s very exciting. It’s really, really great.”