Whatever you do, it can all be for nothing if you don’t install a security camera so you can capture them in the act.
As I understand, security cameras are now very inexpensive. If you can, make sure the camera is in your house so no one can just take it away. Also, if possible, I would try to have the recording medium off your premises. That may be more expensive than it sounds. But if someone can slash your tires, they may decided to come into your home and bring their stupidity into your home. It would be a real shame if they did anything to you in your home (for which they could go to prison for a very long time) if they could just remove a tape or disk from your recording device so that you could not prove it.
It would be so sad if you recorded them doing something that should send them to prison but they just steal the tape or disk on which you recorded it. If the recorder sends the images to some place away from your home, it would be much better.
I don’t mean to frighten you. The odds that someone who slashed your tires will force their way into your home and do violence to you is extremely low. But if it was me, I would pay the extra cost to ensure that if it every should happen, they could not get out of it just by removing the tape or disk from your home and destroying it.
I sincerely hope that you will be able to capture whoever slashed your tires in the act. Then, I would hire a lawyer to handle contacting the police.
IMHO, it is so much better to have a lawyer represent you when talking with the police. There are many reasons for that. If you just walk into a police station with your evidence in hand, you can never tell just who you will wind up dealing with or what their attitude will be. They may have problems with your gender or your race or any one of many other attributes.
But a good criminal lawyer will likely know a police detective who will be sympathetic to your problem and who will want to help you. Also, if you just walk into a police station and you are not taken seriously, what would you do? A lawyer would know how to get the police to take you seriously and they would know what to do.
Best of luck to you. It really angers me to hear that some coward would come by when no one can see them and slash your tires. Someone who does that is not likely going to be someone you can reason with.
I hope you can arrange for them to spend a very long time in prison. Long enough so that if and when they ever get out, they will be too old to ever do this sort of thing again.
P.S. If I lived in the USA in 2015, I would def have a serious weapon in my home so I could defend myself. The most important thing to do when you have a weapon at home is to do whatever is necessary to ensure you are well trained in how to use it. I know most people might disagree with me about this. I guess I should say this is just my opinion.