Taiho Shichau zo (TV)

Very similar settings. Both are about daily life of Police officers and have a good balance of slice of life comedy and action. Very lighthearted and the only noticeable difference is that one has Mechs in it.  

Both have the same situation where it involves teens doing public safety. 

The synopsis of "Hakozume: Koban Joshi no Gyakushuu" reads like that of the anime "Taiho Shichau zo (TV)". That's why I would like to recommend the policewoman duo Natsumi and Miyuki to you. In both series we accompany the main characters on their adventures in the police service. "Taiho Shichau zo" is from 1996, but the series has a great drawing style. The mangaka of the original Fujishima Kōsuke is a fan of cars and motorbikes, so the drawings are very detailed. Moreover, automotive history is represented here, from the BMW 3 to Ferrari Maranello and Toyota Supra. Personally, I particularly like the character of Kobayakawa Miyuki. She is a passionate mechanic and has good taste, her car is a Toyota Sports 800. The series "Taiho" is very funny, action-packed, with curious cases and sometimes with serious undertones. The characters are likeable and overall the graphics are great, especially the animation of the car chases was ahead of its time. Musically, both series have a great soundtrack to offer and the voices for the VAs are well chosen in each case. I particularly liked the voice of Hiramatsu Akiko, who speaks Miyuki. The series "Taiho Shichau zo" has four OVAs and five TV adaptations with a total of 123 episodes that followed later. My recommendation, watch the OVAs and if you like them, I'm sure you'll like the series too. Thanks for reading and have fun watching. read more 

Same creator. Same vibes. Both have the same type of light and warm comedy. Megami-sama is more oriented on romance comedy but there's also some in You're under arrest. Also both shows have similar art and loveable characters. Except the magic setting and police setting they both give a really similar feeling.  

Both are about catching criminals on the road, 2 female partners one of them love cars.. they are kind of the same.. 

Although in Daphne they're not a police force, but some sort of odd jobs mercenaries, the kind of missions they do are similar to You're under arrest's. 

Both revolve around attractive female lead(s) who work for/with police trying to keep their cities safe, Yuugen Kaisha(or "Phantom Quest Corp" as I first knew it) has a supernatural theme to it while You're Under Arrest is more "slice-of-life" like. Adventure, comedy, action and little romance can all be found in both series. Both from 1995/6 with decent graphics and added bonus: good dubs. Worth noting "Yuugen Kaisha" has only 4 episodes while "You're Under Arrest" complete TV series has 96+ episodes excluding the movie, OVAs and specials. I think if you liked one you will like the other. 

both are law and order comedy animes from the 90's with similar art  

You may find Aoi-chan from YUA very similar to Mizuho-san from Otome wa Boku ni Koishiteru ^^ Both gentle, pretty and very romantic but may be rough on they who brings evil ^_^