Educating kids about problems they would face with lying to others is something you should be doing as part of school academics. While you may be teaching moral values by discussing several stories each covering different moral values you should always ensure that they are following these moral values in class. However, in cities or in some schools were there are kids from rich families there would be a situation where these rich kids would be doing mistakes but would be pushing their mischievous activities on other students in class. While you know truth you could not blindly argue with elders in such families about what their kids are doing in school. You would need strong evidence to make elders of that family understand sort of mistakes that they are doing in growing their children in right path.
You do not have to ask cops to register a report and submit file in court. You could approach liedetectors.co.uk and ask them to check if students whom your school staff are suspecting are real culprit of things that are happening in school. Once you have proofs then you could warn parents as well as students from doing such things in your school. Also, you could make it clear for all students that anyone who do not follow rules in school would be punished a lot and every sort of activity they do would be easily identified by school staff with help of experts from lie detecting company.
You could also appoint a full time service expert for your school so that parents would understand how best you are planning for bright future of students studying in your school. Also, you could reward students who have always been obedient and have always been telling truth.