They used to use peer-to-peer to speed up music download (and reduce the load on their servers, presumably) but I believe that it is no longer the case: https://torrentfreak.com/spotify-starts-shutting-down-its-ma...

Actually it's mentioned in the article itself: "The technology deployed by Spotify was also familiar. Like the majority of ‘pirate’ platforms at the time, Spotify operated a peer-to-peer (P2P) system which grew to become one of the largest on the Internet. It was shut down in 2011."

The date appears to be wrong though, since the other sources (including the linked article) are from 2014.