Support reps can send an email to any contact when they have added a new comment to a case.
Case Comments (Related List on Case Detail Page) > New
Currently we don’t see Send Email Notification option.
Setup > Customize > Case > Support Settings
Support Settings > Enable Case Comment Notification to Contacts
When Case Comment Notification to Contacts is enabled Case Comment Template field becomes visible. Select the email template you want to use while sending case comment email.
Now we can Send Customer Notification is available in case comment.