According to China's "Regulations on Procedures of Public Security Organs Handling Criminal Cases":
Article 166 A public security organ shall immediately accept a citizen's abduction, report, complaint, report or the criminal suspect's voluntary surrender, inquire about the situation and make a record. After verification, the abductor, informant, accuser, prosecutor and surrenderer shall sign and press their fingerprints. When necessary, audio or video recordings shall be made.
Article 167 The public security organ shall register the relevant evidential materials provided by the kidnappers, informants, accusers, prosecutors and surrenders, and make a list of evidential materials to be accepted, which shall be signed by the kidnappers, informants, accusers and surrenders. When necessary, photographs shall be taken or audio or video recordings shall be made, and they shall be properly kept.
In other words, whether the public security organ files a case for investigation has nothing to do with whether it is fingerprinted. Fingerprint is a procedural problem.