Are you looking for the functionality which will help you to automatically send an email once a case is filed into CRM?
Yes, you can implement this in CRM. You just need to write one Table Level Script (TLS) for the case. The TLS will fetch the person attached with currently created case and then accordingly send the email notification respectively. We can do the same at the time of case closed, too.
While sending the mail, just make sure that you have a valid “Outgoing mail server (SMTP)” within your email configuration settings.