That cute little rainbow rabbit might hop on past without delivering the free, ultrafast Internet your neighborhood school, library or police station was hoping to score.

An arrangement with Google allows for many area public buildings to be wired for free if enough households around them pay $10 to pre-register. So far, 66 areas have met their goals, out of more than 200.

Here are a few of the entities that might miss out by not having enough registrations to trigger the free access: the Kansas City, Kan., school district’s Central Office and Training Center; Kansas City Kansas Community College Technical Education Center; Hogan Prep Academy; Turner High School; Schlagle High School; and the West Wyandotte Library.

The list goes on and on, with places on both sides of the state line.

Take the example of a Missouri “fiberhood” dubbed South Town Fork Creek. No one has signed up for Google Fiber in that area. Zero. Zilch.

So the nearby Southeast Branch of the Kansas City Public Library might not get access, unless 67 people pre-register before Sept. 9.

Google set up this inequitable handing out of the fiber goods by tying the opportunity for free access for public spaces to the whims and tech savvy of the surrounding homeowners.

The thresholds for gaining free access for institutions differ from area to area, depending on population density and difficulty factors with the connections.

Problem is, public school districts like Kansas City, Kan., can’t promote Google without risking the wrath of Time Warner Cable, AT&T and other competitors. Yet they risk having some schools wired for ultra-fast access and others, generally the poorest schools, not.

“I’m not sure everybody has thought through all the implications of what it means to support it and how to do it in ways that are equitable,” said David Smith, a spokesman for the district.

So the civic-minded are becoming pitchmen for the bunny to take advantage of the freebies Google is dangling. It’s a brilliant strategy by Google. Why market when you can get paying customers (including columnists) to do it for you?

I’ll hop along. If it increases the chances of free access for schools, libraries and other entities, especially in areas underserved digitally.

One effort by the Social Media Club of Kansas City is pressing for philanthropic souls to pony up enough preregistration cash to tip areas over the goals preset by Google.

Ultimately, Google needs the customer base willing to pay monthly fees and installation costs — breathing, paying customers. But if there aren’t enough preregistrations in some areas, the bunny moves on. It’s a now-or-never deal.

And that’s the sorry sight of a bunny turning high tail on some significant portions of the metro area.