My father said i stole money out of his backpack.

You can absolutely be charged, and realistically speaking to the police can help them charge you.  I generally recommend against speaking to the police unless you have counsel present.  Even a denial if done improperly can boost the case for the prosecution.  I am surprised the police are actually investigating something like this but they may have their reasons.  Essentially this case is going to boil down to he said you said.  It's a tough case for the prosecution under the best of circumstances be careful not to inadvertantly make it an easier case by giving them a statement that they can use against you.  Your best bet is to sit down with local counsel and go through everything.  Let them talk to the police for you or if an interview is a must let them be present with you when you make your statement.