I have a Sitecore instance using Dynamics CRM within the follow ConnectionStrings.config
<add name="Dynamics-2011" connectionString="url=http://crmdevvm:5555/crmdev/XRMServices/2011/Organization.svc; user id=domain\Myaccount;password=P@ssw0rd;organization=crmdev;authentication type=0" />
As this is a development environment, the user MyAccount has System Administrator permission (Security Role) in CRM.
Now, this needs to go to Production and I wonder which permission level would be necessary to keep things up & running without messing up with the communication between Sitecore and CRM.