Some time ago now, there was a short polemic published on the Socialist Party in relation to the police and the state (Marxism and the State: An Exchange). The protagonist of the debate, a by then ex member of the Socialist Party had criticised the Socialist Party for its position in relation to the police, regarding that he believed the police were reactionary through and through and therefore Marxists shouldn't make appeals to them.
As the reply admitted, the police are often used to crush the workers movement and are used by the state as a tool for repression. Thus some people come to a position that the police are 'one reactionary mass'. But this is only one side of the situation. Any institution is made of human material and such peoples opinions, beliefs etc change over time. Of course, the impact of their day to day activities is important, but so is the wider world.
As people may be aware, the 1918-19 British Police Strikes were led by Socialists within the police force - now it may be objected that this was a unusual situation - but the reply in the polemic gives several others - such as Emil Eichorn taking over the Berlin police without arguement and the paralysis of the police during the May 1968 events in France. (Also, the 1917 overthrow of the Tsar was conveyed by a very excited Kharkov police chief, as Trotsky notes in The History of the Russian Revolution, chapter 8)
I'd like to add one more, in his book German Revolution 1917-1923, Pierre Broue points out that "... the Communists stepped up their propaganda work towards non-proletarian layers affected by the crisis, in particular officers and policeman."(pg729)
This was in 1923, during the hyper-inflation crisis, when if anything people were turning towards the nationalists in Germany (the Communists experienced growth too, but at a somewhat slower pace). Why approach the police? Because they aren't seperate from the class contradictions that tear through societies.