Hyper Police

Hyper Police is a 1993-2004 manga and 1997 anime series, set in the twenty-second year of the new Holy Century, in a post-apocalyptic Tokyo city, where humanity is an endangered species.

Quoting from Wikipedia: "The anime takes place in the year 22 HC (Holy Century), in the Tokyo ward of Shinjuku. Although theoretically about the competition of rival private police corporations (licensed bounty hunting firms) in an Earth where humanity is in danger of extinction, in actuality it focuses more on the lives of the main characters, such as; Natsuki Sasahara, Sakura Bokuseiinmonzeninari, and Batanen Fujioka. The monsters are usually taken from Japanese mythology, updated for the modern era."

Tropes used in Hyper Police include:

Action Girl: Naoko Kondo.
After the End: Many buildings are still destroyed. Other parts of the city, however, have been rebuilt or weren't damaged in the first place.
All Men Are Perverts
An Ice Person: Poe
Attention Deficit Ooh Shiny: Natsuki.
Babies Ever After: Tommy and Poe get together and have nineteen kids...er, pups. That vagina is now ground zero.
Big Brother Instinct: Batanen with respect to Natsuki.
Bounty Hunter: What the main characters and their rivals are.
But Not Too Foreign: Sakura is from Osaka, which is, as far as anyone's concerned, out in the boondocks. Natsuki is half (Ancient) Egyptian.
Cannot Spit It Out: Batanen with regard to Natsuki.
Conveniently an Orphan: Natsuki's father is an archaeologist, so he spends most of his time away.
Catgirl: Natsuki.
Cat Smile: Oh, you should know this by now.
Cleaning Up Romantic Loose Ends: Batanen and Natsuki, Tommy and Poe, and Sakura and Sakunoshin.
Cute Little Fangs: All the monster-people protagonists.
Da Chief: ...is a [minor] god. He is, however, never taken seriously.
Defrosting Ice Queen: Poe
The Ditz: Natsuki.
Ecchi: Either it is, or it's doing a pretty good imitation.
Fan Service: Among many other things, the female police uniforms. Then there's the proposed "update" by Natsuki's boss.
Fantastic Racism: Naoko and Fonne.
Fantasy Kitchen Sink: Loads and loads of Japanese folklore.
Fish Out of Temporal Water: Sakunoshin.
Frothy Mugs of Water: Justified for obvious reasons: Natsuki drinks milk laced with catnip.
Furry Fandom - one of the few anime embraced by Furry Fandom.
God in Human Form: Natsuki's mom is Bast. Mudagami is a minor god with the ability to teleport.
Handsome Lech: Batanen.
Happily Ever After: Played straight.
Half-Human Hybrid: The main characters. Natsuki's dad is a bonafide human. Sakura had a human ancestor.
Healing Factor: In the first episode, Natsuki inadvertantly shoots Batanen right in the head. He shrugs it off as a minor injury and quips that he'll be right as rain by the next full moon, then uses it as an excuse to heckle the nurses for the next several episodes.
Henpecked Husband: Mudagami.
Human Mom, Nonhuman Dad: Inverted for Natsuki: human dad, non-human mom.
The Idiot From Osaka: Sakura. Her Osakan accent is so thick even non-Japanese speakers can pick up on it. The dub used an over the top Scarlet O'Hara southern accent
Inferred Holocaust: How humanity got where it is.
Interspecies Romance: More like lust.
Kissing Cousins: Tommy and Batanen are cousins. In the manga, one of Tommy's very first scenes features Batanen dragging him a shower to blow off some steam.
Law Enforcement, Inc.: It's unclear if all police are bounty hunters or not; there are signs of an official police force, but it isn't really expanded on.
Loyal Animal Companion: Natsuki's cat, Bob. Inverted in that Bob is actually older than she is, and is her legal guardian when her father is away.
Kansai Regional Accent: Sakura's is especially thick! Even non-Japanese speakers can pick it out.
May-December Romance: Natsuki is 17; Batanen is 35.
Mayfly-December Romance: Sakura and Sakunoshin.
Mundane Fantastic
Nuclear Weapons Taboo: You just know "human folly" in the opening credits refers to nukes. This is, however, never explicitly stated.
Orichalcum: Natsuki's sword.
Overly Long Name: Sakura Bokuseiinmonzeninari. Dare you to say that 3 times fast.
Perpetual Poverty: The company's finances need to be tightened up.
Petting Zoo People: The 10% variety and, bizarrely, the more zoomorphic kinds, even on the same family tree.
Reading Your Rights: Used word-for-word, but Played for Laughs when Natsuki has to check her card to remind herself of how to finish it.
Really Seven Hundred Years Old: Sakura is 191 years old. Since she looks 19, it is suggested Kitsune just age very slowly.
Reincarnation Romance: Sakura is the reincarnation of Sakunoshin's lover.
Shock and Awe: Natsuki's power.
Shout-Out: Kondo calls Natsuki "Hello Kitty" on page 18 of volume 1, when the two meet for the first time. After snarking about being partnered with the Catgirl, of course.
Sitcom: Despite having some of the trappings of a Police Procedural, the series is this.
Space Jews: Sakura is from Osaka, ergo she is a crafty trickster spirit that robs and kills people to absorb their powers, and is a stingy haggler of epic proportions.
Spell My Name with an "S": Tommy/Tomy, Poe/Peau, Samantha/Samansa etc.
Sunglasses at Night: Batanen.
Super Drowning Skills: For a water/ice elemental, Poe can't swim for crap.
Ten-Minute Retirement: Happens to Natsuki.
What Do You Mean It's Not Awesome?: Batanen laments Natsuki's posing and yammering...which costs her valuable reaction time.
What Measure Is a Non-Cute?