From my experience the easiest way to see if your Windows 8 app needs a privacy policy is to open the Package.appmanifest file and go to the Capabilities tab.  If Internet (Client) is checked you could gather information from the user, so you'll need a privacy policy.

Updated 8/1 - Great comments from MikeSchlichting.  Mike pointed out the following

“If your app has the technical ability to transmit data, you must maintain a privacy policy. You must provide access to your privacy policy in the Description page of your app, as well as in the app’s settings as displayed in the Windows Settings charm.

App capability declarations that make your app network-capable include: internetClient, internetClientServer and privateNetworkClientServer.”