The original poster has put forward a scenario about making a false statement in an affidavit that is used in court proceedings. The relevant offence
is perjury. The exact definition may differ from jurisdiction to jurisdiction but generally speaking: A person who in, or in connection with any judicial proceeding makes a false statement on oath or affirmation concerning any matter which is material to the proceeding whilst knowing that statement to be false or believing it to not be true.
Filing a sworn affidavit that is then used in court (judicial proceeding) that is false definitely is perjury. An easy example is: Filing an affidavit saying that your weekly income is $2000, when it is in fact, $3000. It ought to be noted though that this isn't all that needs to be proven.
To be found guilty, the police need to charge them.
Incorrect - The DPP or AG can also bring charge for perjury.
Police hardly ever charge anyone with perjury.
Where did you source this information from? Perjury, along with a similarly related offence of pervert the course of justice is utilized quite often.