Kidou Keisatsu Patlabor

Redhead tomboy cop protagonist who's obsessed with her giant mechanical vehicle. Part of a schlubby police department that tends to cause more collateral damage that it prevents. Sound familiar? You can basically think of the whole Tank Police franchise as a more crazy and action-packed version of Patlabor. 

A mechanized (Patlabor: Humanoid mechas, Dominion: Tanks) special police unit fighting crime. There are more similarities than you can shake a stick at. MC is a red head tomboy who loves mechanical engineering, slapstick humor, comedy based on slapstick and the good guys doing more damage than the villains. Many side character designs are also similar. The differences are: Dominion is even less serious and has more daring jokes (e.g. torture as slapstick scene, twice!), sexy catgirls, less realistic action and fights leaning towards cartoonish. 

An (over) enthusiastic young woman joins a testosterone-filled police squad in a world where law enforcement regularly use weaponised machines to help keep the peace. These OVAs from the late 80s are full of goofy police comedy and fun action. 

Both are comedic OVAs about the daily lives of a quirky police squad. While Patlabor becomes darker and more serious over time, You're Under Arrest remains purely light hearted. 

Like Patlabor, Full Metal Panic is an action comedy that takes on the concept of mecha in the modern world. Like Patlabor, FMP also mixes Slice of Life comedy episodes within an overarching pot, so you get to see the characters in a variety of situations. Patlabor and FMP also have the same type of mecha. You'll have fun with this one!