You'll need to think carefully about the philosophy of this nation. Fascism is often used just as a synonym for bully, but it has its own intellectual tradition which is completely unique and weird. You need to make an effort to really see beyond the cliches and into the soul of their beliefs. That will help you create believable reasons why the police are behaving so oddly.
The functionality of the Nazi state was for the most part anarchic. Which is funnily enough how your police are behaving! For example... Hitler's office in Berlin received mail in five different rooms, and the person occupying each room would respond to letters, effectively forming policy according to their own design, signing the letters implying Hitler's approval. After all, it was a letter from his office.
Hitler almost never actually visited his office, and didn't care for details. Meetings with his senior staff would involve him rambling about any given topic, and his subordinates listening intently before leaving to try and put these ideas into action. He cared only for what he thought were ambitious, brave, or radical ideas being implemented quickly and effectively.
German policy in Poland is a perfect example of this organised chaos, with similarly horrible results. Occupied Poland was divided into three regions, roughly speaking; north, west, and east. Each had its own governor, and they were all told to Germanise their regions. Hitler said he wanted it done quickly, and would not ask questions about how this was achieved.
While the governors of the west and east began genocides, the governor of the north decided that the quickest solution was to give everyone German citizenship. Even though officially the Nazis believed the Poles to be subhuman. True to his word, Hitler didn't ask, and was delighted that the governor had achieved a successful Germanisation so quickly. This led to the horribly warped reality that half of one family living in the north became Germans, while their relatives living in the south were sent to death camps.
The even stranger aspect of this was that Heinrich Himmler threatened the governor, saying that as just one drop of bad blood would contaminate the master race, his policies were unacceptable. The governor however told Himmler that if he had a problem with it, he should speak to Hitler.
This organised chaos was a direct consequence of fascist ideology, and Hitler's beliefs in particular. Timothy Snyder is a history professor and world expert in this field. In his book "Black Earth" he argues that Hitler's ideology has been misunderstood, and makes no sense as a traditional nationalist philosophy... but makes perfect sense when Hitler is considered to be a 'racial anarchist'. Hitler considered laws and ethics meaningless formalities, which prevent violent competition between 'races'.
One core fascist belief is that each nation provides an opportunity to transcend its people into their own race, which is not the means to an end, but the end in itself. Uniquely, fascists also believe that violence is a moral good in itself. Underlying the bizarre anarchic practices of the Nazi regime was the belief in a social darwinist principle of the survival of the fittest. If a Nazi official thought he should be promoted to replace his superior, he should prove himself fit for the role by seizing power from his superior one way or another.
Police officers behave viciously, because members of the regime truly believe that the laws they follow are at best transitionary restrictions on achieving racial supremacy through violent competition. If you can make violence in your fictional nation consistent with the beliefs and practices I have outlined, and not simply bad because fascism is bad, then you will create a very potent work of fiction that has strong historical and ideological precedent.
For further reading on fascist beliefs, here is an informative article on why Donald Trump is not a fascist according to five domain experts. I would also recommend you try and watch an old BBC documentary, The Nazis: A Warning from History.
