I am looking to send Sitecore analytics data to CRM: if a lead downloads a document, or completes a form, and that lead is KNOWN to both sitecore and CRM, can Sitecore send data to CRM to indicate that this event/behaviour has occured.
Below is an exact problem I have encountered but do not have a solution: https://social.microsoft.com/Forums/en-US/7da6c0fa-6e40-47fe-af30-4126c8936f7f/crm-integration-with-sitecore-using-sdk-and-crm-online-lead-activity-andor-behaviours?forum=crm
It is possible, but will require custom coding. I recently implemented something like this by using the API provided by the CRM (in my case the CRM had rest services that I could use). How and where to code this depends on your solution of course - e.g. if you use wffm for the form you could add a custom save action.
One thing you will need is an identifier of the crm contact in Sitecore - could be the email address. Otherwise your Sitecore application doesn't know which CRM contact to use.
Sitecore does provide CRM integration as well: in case your CRM would be Microsoft Dynamics you can download a Connector here: https://dev.sitecore.net/Downloads/Dynamics_CRM_Connect.aspx (some more documentation here: https://doc.sitecore.net/CRM%20Connect/12). Or you can use this information to build your own. But that might be overkill if you just need to send an event...