When responding to criticisms from the people of your jurisdiction, it would be best to answer by showing them that you are doing your best in solving the cases presented. Show them that the investigation is moving and if you encounter problems, you should also ask them to cooperate.
Thinking about filing cases against those who criticize you will not help. It will make you look worse.
Remember, you answer to the people, not the other way around.
I my humble opionion (IMHO).
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7 summoned for criticizing police on Facebook https://technology.inquirer.net