In order to connect Constant Contact to external integrations, you would have to have the 'Email Plus' version of Constant Contact, which would allow you to create users within Constant Contact. You would then have to create a user within Constant Contact.
Once you have the 'Email Plus' version activated, you can go into Constant Contact, click on your name in the upper-right corner, then select 'My Account'. From this area, you can select 'Add Users' and create a user that you can then use for external integrations.