By default, Jetpack's Contact form will send an email notification to the post or page author. You can change the default behaviour, and even send emails to multiple email addresses by going to the "Email Notifications" tab in the form builder:
http://jetpack.me/support/contact-form/#jp-carousel-723
Once you add an email address there, you'll need to click on "Save and go back to forum builder", and then on "Add this form to your post" to update the existing form.
I hope this helps.