Jackrabbit does not integrate with any customer relationship management systems.
When emails are sent to families through Jackrabbit, a copy of the email is saved to the Family record > Misc tab > View Sent Emails for a period of 365 days.
You are able to easily export the contact information from your Jackrabbit database using the Email Listing Report (from the Reports menu > Families/Students category). From there you can import your data into an email marketing service such as Constant Contact or MailChimp.