Usually, Sweden's public libraries are run by the individual municipalities (kommuner). Some municipalities only have one library, while some have several libraries connected with one another to some extent. For instance, in most municipalities with several libraries you can borrow and return books at any of the libraries within their organization.
When it comes to purchasing books, that can vary between different libraries. In some organization's you might have one librarian, or a group of librarians, who buy for all libraries within the municipality, but I think it's more common for the person/s in charge of purchases to buy books for just their local library. Libraries can be very different, even within a municipality, which is something to take into consideration when getting new books. That which is purchased for one library, may not be neccessary at another library, so it's very individual for each library which books to buy.