It may well be the $40 million gift horse.

In April, Joshua P. Rechnitz pledged that amount — the largest single gift in the history of New York City’s parks system — to build a field house in Brooklyn Bridge Park.

The gift was heralded as a much-needed boost for the 85-acre waterfront park, which is still under development. But attention quickly turned to the centerpiece of the plan: a velodrome with a 200-meter inclined indoor cycling track and stadium seating for almost 2,500 spectators. At the track’s center would be limited space for more traditional sports like basketball, gymnastics or tennis.

Now, some parkgoers, neighborhood activists and community leaders are looking that donation in the mouth and saying, Thanks, but no thanks.

Leaders of the major community groups in the neighborhoods abutting the park, including Brooklyn Heights and Dumbo, have questions about the track. They say they worry about the building’s size (with a footprint of up to 70,000 square feet, it is larger than a football field) and the traffic it might draw to the cobbled streets of Brooklyn Heights, while pointing out the relatively obscure nature of track cycling, in which riders on fixed-gear bicycles without brakes travel at terrific speeds around curves banked at 45-degree angles.