Yes, charges can be filed for trespassing (or any other crime) even if the property owner does not file charges. Criminal law is not like civil (i.e. lawsuit) law: in a civil case, a person sues for compensation for an injury, loss, etc. done to him or her. If the person who suffered the loss or injury chooses to not sue (is willing to not be compensated), then no can take action for him or her. It's like if you loan Bob money, and Bob refuses to repay you; your friend Jane may be outraged on your behalf, but if you are willing to let Bob keep your money, Jane can do nothing about that.But criminal law punishes people for violating society's laws; it is society, not the person to whom the crime was done, that has the interest in enforcing the law and the power to do so. That is why criminal cases are always titled or captioned "State vs."--it is the state, or the government, not the person who was wronged, bringing the case. So the state police can file charges to enforce the no-trespassing or other laws even if the property owner doesn't want that done.