Does it constitute a criminal offence for non-public security organs to use network IP addresses to collect other people's computer information privately?

First of all, it depends on the case, such as some special cases, such as corruption, and the procuratorial organs also have the right to investigate.

The second is to see if its procedures are legal.

Again, it depends on whether this behavior has caused serious consequences.

It cannot be defined as a crime, and there is no perfect legal provision for this kind of cyber crime in China at present. Besides, it is difficult for your client to grasp the evidence, let alone a state organ.