Half-Life: Full Life Consequences: Not only does the only cop to appear try to give John Freeman a ticket for speeding (when he is trying to rescue Gordon Freeman), but he is headcrab zombie as well!
Superwomen of Eva 2: Lone Heir of Krypton: When the Section-2 agents (the security detail tasked with watching and protecting the pilots) are not busy with harassing, torturing or assassinating witnesses, they are highly incompetent. Asuka can very easily slip her bodyguards, even without her superpowers. And a terrorist group was capable of abducing Shinji despite of them.
The rest of the Superwomen of Eva series doesn't improves on their portrayal, with them being pretty much Gendo Ikari's Kick the Dog goon squad-slash-Secret Police to enforce The Scenario's route and the loyalty of those who are important to it (as an example: after Shinji talks against Gendo's standing orders to kill the Superwomen on sight in Superwomen of Eva: Lilith's Herald, Gendo simply has Section-2 beat him within an inch of his life and then displayed on NERV Headquarters as an example of what will happen if anybody attempts to defy him).
legolas by laura: Technically they're not police, but the guards - sorry, ''gards'' - assigned to protect Laura are thoroughly useless. The orcs sent to kidnap Laura get in, get out and get all the way back to Mordor before they tell Legolas that Laura was taken. Even then, Legolas had to ask first.
The is played with in Kill la Kill AU.In one of the fanfics, when Ragyo suggested calling the police to find a kidnapped Ryuuko, Nui says, "What the-?! No, don't call the police, the last time we had called the police they arrested Ryuuko and not the person that stole that piss couch which is why we had to get a new one and, besides, the police are terrible at finding missing kids, 'cause they haven't found those other missing kids and there are one-hundred of them besides Ryuu in this city alone." Which would make that played straight, particularly when Satsuki actually confirms this. Otherwise averted when they had thrown Ryuuko in jail for truancy in an earlier comic, showing they do enforce laws.
This is subverted in Petrification Proliferation where it is actually illegal to NOT report the presence of a Basilisk to the Ministry, due to them being considered as Weapons of Mass Destruction. The Department of Magical Law Enforcement promptly shuts down the school in order to check for other potential threats.
Mega Man: Defender of the Human Race subverts it as the story goes on. Initially, the police are useless because they didn't have the weaponry or experience to take on Robot Masters. As the story progresses, we see they're still perfectly good at fighting regular crimes and eventually upgrade their gear to fight Dr. Wily. Mega Man collaborates with the police to minimize casualties and the cops even saved Mega Man's life once when the Mega Man Killers were about to live up to their name.
When things get especially horrifying for Darci in Claire the Kind, her first instinct is to call her detective father, only for something to shoot it down (either by one of the others taking her phone or talking her out of it). Justified, considering that local law enforcement would be in no way equipped to deal with trolls, and it would make them sound insane if they even tried.
Missing Linc: The police make no attempt to interfere with Lisa's interrogations of Flip and Tetherby. While she is grateful for this (as it allows her to investigate without interruptions), she also plans to write to the mayor and complain about it.
Subverted in Desperately Seeking Ranma, as the police know the kind of things that Ranma and his friends fight off are way out of their league, so do what they can to channel civilians out of the way, and dont give them too much hassle about minor collateral damage.