though my general unfamiliarity with the US justice system may falsify that statement.
Who lays criminal charges? Is anyone allowed to, or only the prosecutor's office? Here in Canada, the laying of criminal charges is under the sole purview of the Crown. However, that doesn't mean that it's under the sole purview of the state in your system.
Perjury, being a crime, would have to be brought forth by the Crown attorney here. Further, criminal law is the under the sole purview of the Federal level of the government, not the provinces: provinces do not and cannot lay criminal charges. I would imagine that it's similar there in that only the state (and not individuals) can lay criminal charges, but (IIUC) it's actually up in the air as to which level of the state can lay charges; for some things it's the Federal level, while for others the State level. So, in order for the policeman to be charged with perjury, the Attorney General of either the United States of America or the State of New York will have to decide that it's likely that the policeman would be indicted, that the policeman would be convicted, and finally that it's advisable to do so. This seems unlikely to come from the Federal level (after all, the policeman was basically acting on his behalf as a Republican when he was hassling the protestors, and given the general odour that Those Uppity Liberal Commie Pinko Faggot Professional Inciters are held by the junta in power), and unlikely from the State level as well (as the State Attorney General probably doesn't want to alienate the policeman's union, considering how dependent he is on evidence gathered by its members for the rest of his work).
Gotta realise the difference between civil and criminal law, you know, and perjury is a criminal matter, not a civil matter.