When you import petition signatures into NationBuilder, there are two ways to connect the signatories to an identical NationBuilder petition: first, tag all of the external signatories with the same tag as people who sign your NationBuilder petition. Make sure you're tagging signers of your NationBuilder petition by editing the petition page and checking the Petition > Settings page. The tag goes in the text field under "Tag the signer with"

By having a unique tag for people who sign this petition, you can communicate with all petition signers at the same time regardless of where they signed the petition. 

Next, update the total number of signers on your petition. This can be done from the same Petition > Settings page:

These two steps will let your community know how close you are to your signature goal and allow you to communicate with signers simultaneously. Two caveats: The signatories from another site or collected offline will not display in the activity stream of the live NationBuilder petition. And the total petition signers will be available when sorting on the unique petition tag - signatories from another site or imported as a CSV file will not be listed on the Petition > Signatures page.