No, you do not issue a CAR. A CAR is issued as a result of a nonconformity when root cause analysis is often required. All you need to do is inform (via email) the affected parties of the changed document and the nature of the change. Then you request a confirmation. BTW, there's document control software that can do all this for you!
What if in situations where confirmation is not an option from different folks involve. I mean when disagreements or arguments arise?
I am using SharePoint server for change request/approvals.