Sort of. Even if they don't carry them on their belts, I'm sure your police have access to them. They do need to be prepared to protect their civilians in case the unimaginable happens. Our police don't all walk around with shotguns and such if that's the impression outsiders get, although all of them do have a handgun on their belts, which is strapped securely into their holsters. They don't get taken out unless the officer feels his life is directly threatened.
I've actually got a story about my small hometown that really sums this all up. It's such a small quiet place, that when we had our only gun crime in ten or fifteen years, our police officers didn't actually know what to do. A doctor with a latent mental disorder snapped and held his wife hostage with a gun. Our officers all carry handguns in their belts at all times, but when push came to shove, backup from larger cities and a special team needed to be called in to deal with the unimaginable because our officers never use their guns, ever.
The few and far between instances of police brutality that make the news can't really throw off our perception of our officers, who are mostly average joes, your uncles and such.