Twitter app does use my address book? I would like to start using twitter on my smartphone but I do not want to share info with my contacts.

Does Twitter app for android suggest to my contacts to link to my accounts?
In 2012 it was reported Twitter did upload the address book to their servers. Something changed after that. 
In case you're wondering if it has in the past you can visit https://twitter.com/settings/contacts_dashboard

If you are using Android 6.0 or higher you can disable the contact permissions as a extra precaution. 

The Twitter app doesn't use your contacts unless you explicitly enable this in the settings of the app. Only way to identifies you with others that have is through your email (and mobile number)