I have a lot of retailers tell me they connect their Facebook page to automatically update their Twitter profile whenever they post something on Facebook.
I suggest this only if you are logging into Twitter (or through HootSuite) every day and still participating in the real-time conversation, and responding to anyone who might have mentioned or RTed you.
The reason you would connect your Facebook page to Twitter is to save some time. If the content you post on Facebook is content you want to share on Twitter, then this is a good option. However just keep in mind it will share every post, so don’t double post unless you’re posting on Twitter at a different time than Facebook.
To set this up if you haven’t done so already, go to http://facebook.com/twitter, find your Facebook page and click ‘Link to Twitter.’
If you already have these linked but never log in to Twitter to RT others, comment back, ask q’s, etc., then I suggest you unlink these accounts as it looks like you don’t care about anyone else on Twitter, you only care about the things you want to talk about/promote. To unlink, go to the same link above, find your page and click “Unlink from Twitter”.