Thanks for the feedback everyone! Yes, I was thinking it was just some sort of screening tool that was used due to the short duration. Good to know that it shouldn't interfere with getting an accurate result on any future testing. If we stay in the public school setting, he wouldn't receive any more testing for over 2 years anyway. But if we decide to apply to a different school, he might need some testing sooner (for example, there is one "accelerated curriculum" private school in our new city, but it's pricey, and I don't know much about it yet). I just really wanted to know what instrument they used, because I feel a little silly passing "scores" along to his new school without knowing how they determined these percentiles. I don't know that the information is relevant anyway to Kindergarten in just a regular public school. Only scenario I can think of that might make the scores useful is if I were trying to persuade them to let him go up a grade or two for math and/or reading. But then they would probably determine that need for themselves using their own assessment.
What would you do? Should I just keep the results to myself until/unless it becomes necessary to share? And then staff from his school could call the district here and try to get more information if they need it? And why do you think the lady at the district office here was so suspicious of me on the phone? All I can think of is maybe some parents try to find out what screening tools are used and then prep their children, so they have to fiercely guard that info?