It is unbelievable that so many people do not apply for this benefit when it is so easy.
When we purchased our co-op in 2004, the previous owner did not have the STAR exemption, so we had to apply for it, which could only be done once a year and we had just missed the deadline. That was a cute discovery. When talking to the town of Greenburgh, they told us that if the previous owner had STAR on the co-op, it would transfer with the co-op. So basically, when we were dealing with it, STAR exemption stuck with the house, not the people, so if the house is exempt, and you purchase it, it will still be on the house assuming you are eligible.
You should definitely be able to receive an answer from the Town of Patterson about this though and should definitely verify it.