To what extent do prosecutors work with/are prosecutors allowed to work with police to investigate crimes?

I'm a 2L (in the U.S.), and I'm currently looking at applying for summer opportunities. Browsing through the website of my local prosecutor's office, I noticed that they have several "investigative" divisions for things like drug charges, homicide, counter-terrorism, etc.

I was under the impression that the police are supposed to allow prosecutors access to their investigative reports, and prosecutors themselves are allowed to review those reports and decide whether to file charges (maybe telling the police what they would need in order to file charges). Maybe it's just poorly named, but having particular investigative divisions for certain kinds of crime seems to be a thing across different DAs offices.

So do prosecutors work more with police than I thought they did? Do they conduct their own investigations, independent of the police?

(I ask because it seems to me that if the police really work closely with prosecutors, I would have some concerns that police would basically act as state-funded investigators for the prosecution, while the defense wouldn't have any investigators at all)