There's no formal approval process other than Apple's — just submit to Apple.
However, make sure you're abiding by libspotify's Terms and Conditions, particularly the fact you can't charge money for an app that uses libspotify.
If you'd like guidance, especially with your UI components (you must make it clear that music is being played from Spotify), contact the same team you would for web apps and they can help — contact details are on the Spotify developer website.