Fun fact: as a regular citizen you can apply for such a permit online. I did this when we were moving houses to ensure the entire block in front of our house would be clear of cars (or we could tow if required) to make it possible to get a moving truck in on the one-lane street where double-parking would block all access. I filled out the forms. A week or so later the city dropped signs on the sidewalk warning of the upcoming closure.

You can also close your entire street for a block party. You just need a certain number of people on your block to sign the form approving it.