Is the Associated Press "some random asshole on the internet?" I'm totally using that one!
Here's how I understand the order of events, viewing them as favorably as I can to CPS:
1) Get tip
2) Tip results in some concern
3) Get scared enough to take four police officers to house
4) Ask to inspect
5) Get told "no"
6) Give up
Given the fact that there was no follow up, I think there are only two logical conclusions here: A) CPS (or its NJ equivalent) didn't really believe there was a threat or B) They believed there was a threat, got turned away and gave up.
I can't see any reason to believe anything other than (A).
The AP hasn't given an independent version of events, all we have gotten is a description from a person with a vested interest in making themselves look as good as possible and making their cause look under threat as much as possible.
I don't see a reason to pick A over B. When the man said they didn't have a search warrant, and, for that matter just happened to have a high powered lawyer with a background in gun rights and legislation on call for exactly this (which is pretty convenient, honestly) on the line monitoring the whole situation, unless the police saw something then and there that gave them probable cause to push further, it is entirely possible the police/CPS were unable to make a determination as to whether there was a threat or thought there might be but had insufficient cause to pursue the matter then and there. That they left the premises at that moment doesn't mean this thing is over of CPS thinks there is an issue.
I honestly don't expect to ever know what really happened, however, I get the sneaking suspicion that people who are jumping to take this at face value are largely doing it because it validates their existing worldview rather than any objective analysis of the facts.