You don't have to apply for it at all. The owner of the park is supposed to distribute any credits. Read through the information on the PDF link I posted and contact that agency with any further questions.
They simply do not know which I think is ridiculous. It could just be certain representatives that just did not know. Another agency says "yes, you would have had to apply and/or register with the assessor's office." Another says something different. A couple of people said that STAR is not even considered a tax matter. - 240 people in one park never knew about the STAR until their landlord told them all about it. There are so many more people that did not know about it. I am a news buff and I am also human. I did not know about it. Now I do thankfully. I will post back here within a couple of weeks when I have more information because I hope to be able to help someone else.