It is possible to export any contacts, or connections that you have in your LinkedIn account so you can then import them to your Constant Contact account. Please follow their Help Center instruction on exporting connections out of your account. Once you have exported the connection, you can upload that .CSV (Excel spreadsheet) file to Constant Contact.
Just make sure you do have explicit permission from those contacts to add them to your mailing list. I hope that helps!
... View more