Federal grants and city funding is two different things.
Yes -- and a combination of both make up the police budget -- and must be taken into account.
For example if the federal government eliminated a yearly grant then the local Durham police department would need to make the hard decision to fund the four positions out of local general funds or to let the officers go. The general fund police budget each year is built on the basis of what federal funds will be provided.
In the same way the county school system budget is built on funds coming from the federal government, state government, and local government. All three parts encompass the school budget. You don't just consider the local component to be the school budget -- and make claims about the overall school funding. If the local component goes up but the state & federal school budget components drop causing the overall budget to decrease -- you would not claim that the schools are not being defunded because the local budget went up. To do so would be absurd.