The way I interpreted that scene in the novel and the movie was that the police guards and the Corleone guards were removed separately. First, McCluskey has the Corleone men arrested, ostensibly for carrying illegal firearms. (Remember how Tom makes it a point to say that the men he brought in were private detectives licensed to carry weapons.)

Next, the police guards are called away from the hospital to other details; McCluskey possibly told them that others would be coming in shortly after to replace them. Perhaps they would be legitimately coming...only to find that Vito had already been whacked during the time gap. I seem to remember the nurse saying that the police had only been there just a few minutes before Michael turned up.

The nurse probably wouldn't have thought a thing of it, other than she was glad to be relieved of all those men crowding up her hospital. She wouldn't have been a threat to the mob guys. If anything, the mob guys coming to whack Vito would've been told to keep it quiet. Get in, do the job, get out, don't be seen and don't make a lot of noise. Any collateral damage on their part could've easily brought the heat down on McCluskey/Sollozzo.