This is kind of a gray area, but there is a procedure...
Theoretically, the way a runway is closed is that the airport or airfield operator notifies, in writing, the FAA thirty days ahead of time that a publicly-accessible runway will be closed. The FAA then issues a NOTAM about the closure and the airport puts big X's on the runway at either end. The runway is then closed.
In the event of accident, you obviously cannot "close" a runway this way. The best you can do is warn pilots off it. Since there is no way to "close" a runway on a short-term basis, what happens is that they "close" the entire airport, which is what happened at La Guardia. There is no NOTAM or forewarning during the initial response, so small aircraft can potentially still arrive and they have to be warned off.
Unfortunately, a lot of police and firemen do not understand this, so they try to "close" a runway just by ordering the tower to close it. Often, they do not even do this; they just rush onto the tarmac without even waiting to get permission or calling anyone. Obviously this creates incredibly dangerous situations. The tower (if there is one) reacts to this irregular action by notifying ATC and making constant do-not-land-here warnings on the common channel(s). If there is no tower, hopefully there are people on the ground with radios who do the same thing.
Just as an example of how dangerous this can become: once I was at an airfield with no tower and an aircraft landed short in the trees, getting hung up in some branches. A bunch of state police cars and fire engines literally drove down the runway to get to him like it was a road or something. The danger here is that many smaller aircraft or ultralights (etc) may not have (working) radios or may be on the wrong frequency so they have no idea what is happening. They could have just landed on one of the cop cars and blown up killing everybody. After it happened we called the police and told them how to drive on side of the airfield (not down the runway !!!) and provided them with emergency route maps, but at a certain level it is whistling in the dark, because most emergency personnel do not read these materials.