The mailer contained the graphic below, which claimed that the median tax bill was $6,962 in 2011 and in 2016 it was $10,516, an attention-grabbing 51% increase.
It also claimed that the part of the town budget funded by taxes had increased 15.4%. Essentially, this says that the total taxes collected (the levy) only grew by 15.4%, which seemed inconsistent with the 51% increase in the median tax bill.
Reading further, the following statement appeared:
It seemed very unlikely that the median and the average (mean) tax bills would match to the dollar.
I checked our tax bills, and they had not increased by anywhere near 51%, so I began to suspect the numbers in the mailer were wrong.
At the first Town Council meeting in June, I said during public comment that the numbers in the mailer were wrong. I was politely told they were not, and it was suggested that I could set up a meeting with the finance director and she would explain the numbers.
At this time, the position of finance director was in transition, and Councilman Schwager suggested I meet with the tax assessor instead. This made sense because the median tax bill graphic referenced the following footnote:
Subsequently I met with the tax assessor, and it was immediately clear that she had no idea where the numbers in the mailer had come from. She gave me copies of what she had provided to the finance director and town manager, starting with the following email to the IT director at New England Revaluation, the contractor who hosts the town's real estate database:

It was interesting that she had apparently been asked for this on short notice, in the week before the mailer was sent out. The response was:

I put together this YouTube video, which explains why the 51% number is wrong and calculates an estimate using the valuations the tax assessor had given me: