I have created a jotform registration form for an event. Can I share this with another person that needs to be kept updated of the registrants.

Hello pjcraig,

Do you mean to say that you want to just send the registrants data to another user?

Yes it is possible to achieve your requirement by adding a new email alert and set the recipient email to another person's email address. This will send a copy of the submission data to another user. The following guide should help you:

Add new email alert: https://www.jotform.com/help/25-Setting-Up-Email-Notifications 

Set recipient email: https://www.jotform.com/help/41-How-to-Find-and-Change-the-Email-Address-Used-for-Notification-Email 

If you do not want to send submission emails to another email address, alternatively you can also add a "Sub User" in your account and share form with edit or view submission access. This type of users are to assist you in your work. You may like to take a look at the following guide which should help you:  http://www.jotform.com/help/232-How-to-Share-Forms-with-a-Sub-Account-User

Thank you!