Is it useful to appeal to a higher authority if the Public Security Bureau does not file a case?

You can ask the procuratorial organ to supervise the filing of the case.

Although my country's "Criminal Procedure Law" includes criminal case filing activities within the scope of case filing supervision, it is mainly aimed at the situation where the public security organs should file a case but do not. In the absence of specific and clear legal provisions, cases should not be filed, but very serious criminal litigation activities involving the legitimate rights and interests of citizens and legal persons should be included in the scope of case filing supervision. From the perspective of the scope of case filing supervision, especially in our country's cultural background and moral concepts, even if a person is only filed as a criminal suspect by the investigation agency, it will have a considerable negative impact on society.

Article 87 of the "Criminal Procedure Law of the People's Republic of China" stipulates: The People's Procuratorate believes that the public security organs have not opened a case for investigation when it should be opened for investigation, or the victim believes that the public security organs should not open a case for investigation. If a case filed for investigation but not filed for investigation is reported to the People's Procuratorate, the People's Procuratorate shall require the public security organ to explain the reasons for not filing the case. If the People's Procuratorate believes that the public security organ's reasons for not filing a case are untenable, it shall notify the public security organ to file the case, and the public security organ shall file the case after receiving the notification.