Perjury and Falsification

I just want to know lang po about perjury and falsification. What are the difference between the two. I need your help on this matter. The story goes like this.. Our neighbor filed a theft case agaisnt me, according to them I stole a pants. Which I haven't done in my entire life. This was the first time I have experienced this. We've been living in that apartment and in that compound for almost 8 years and they were just living there fo 1 and half year. I am a Teacher by profession for 9 years. We also filed a counter charge then we got a CFA in our baranggay. Unfortunately they don't have their cfa but they were able to filed it directly. We had our hearings and on the third hearing we found out that they falsified a statement of two of their witnesses. I talked to them and they told me na it was not the statement that they've signed and the good thing the respondent gave them a copy which is not same with the statement that they have sworn in the hearing. In short we all found out that they just made that statement para idiin ako sa theft case. They had given us statement proving that it was not the statement that they had signed and they are not the one who made that statement. The problem is now we cannot file the perjury case and the falsification because the witness don't want to give us an authorization for us to file those cases against our neighbor because they are very scared to appear on the hearing and they are so afraid with the respondent. If it was not with them hindi namin malalaman na may falsification. Please help us on what to do? We cannot force them to give us authorization to file a perjury case and falsification dun sa neighbor namin. Paano po namin isasampa ang kaso na yun? Thanks