Yes, you can set up an auto update rule to automatically close a ticket when you send out the reply message.
Step- by- Step Walkthrough:
Step 1. Go to Settings under the Setup tab;
Step 2. Click Auto Update;
Step 3. Click New Auto Follow Up to set up a rule;
Step 4. Set a name for the auto update rule and check Enable;
Step 5. Set When operator replied or forwarded
Step 6. Set "Status equals Close
" as the fields value,;
Note: You can also set value for your custom fields. For how to create custom fields, please click here
Step 7. Save the settings.
You have successfully configured the auto update rule. Now your tickets will automatically get closed after you send out the reply messages.