Did ancient greek cities have any kind of police force?

While there wasn't a police force in the modern sense (which would be the executive part of a tripartite government), we know about some institutions and administrative bodies that are, indeed, comparable. As an example I'm going to look at the quite important Astynomoi Inscription from Pergamon. As all pictures of the inscription available are protected by copyright, I'm just going to start with a description: It's an almost complete limestone slab thats about 1.05 x 0.8 meters big and has four densely inscribed colums on it. While the inscription itself can be dated to the 2nd century AD, there are good reasons to believe that the law which is written down on it originates from the time of the Pergamene kings, probably to the first half of the 2nd century BC. As I said, it's a text which is highly juridical in nature. Let's see what it can tell us:

The whole text is about the rights and obligations of a group of public officials called Astynomoi (from ancient greek ἄστυ (city) and νόμος (law)) and is divided in several paragraphs.
The first paragraph is about the punishment of citizens who build on public property. A fine is specified and it's appointed that the Astynomoi are obliged to enforce it - otherwise they have to pay part of the fine themselves.
The next paragraph states that property owners are responsible for the streets adjacent to their buildings. This affects both repairing and cleaning the streets. The inscription mentions that the streets are divided into several zones and it's possible that each of the Astyonomoi was resposible for the supervision of one of these zones. Again, there are fines defined, both for the delinquents and for the Astynomoi if they don't collect the fines.
The next paragraph still involves the public streets and prohibits to conduct several kinds of works in public which could pullute the streets. It furthermore regulates the contributions to the public garbage collection and, again, defines fines for noncompliance.
The next paragraph is very long and its amount of bureaucracy resembles modern times. It regulates walls, both public walls and boundary walls. It describes the rights and obligations of estate owners, expecially when it comes to building walls on the exact border of the neighbouring parcel of land.
The next paragraph lays down that the Astynomoi are responsible for the cleanliness of public fountains. It is stated that this incudes to punish individuals who illegaly wash clothes or letting cattle drink from the fountains.
The Astynomoi also have a list of all cisterns, also those in private households. Houseowners are obliged to keep the cisterns covered and avoid them to be ill-kept. Apparently the Astynomoi are allowed to examine them regularly.
The last paragraph is about public latrines. It only states that the Astynomoi are responsible for them, unfortunately the inscription is incomplete here, so we don't have any other information.

To conclude: The example of the Pergamene Astynomoi sheds light on the reality of ancient law enforcement. The present inscription mainly deals with problems of the public safety and order and doesn't include criminal acts such as murder and the like. Therefore we shoud understand the Astynomoi in this specific context as a regulatory institution rather than a police force in a modern sense.