At the time, the enclave's three-block-long main drag was known as Prospect Place, a name coined in the 1870s. Unfortunately, there was a considerably longer thoroughfare in Brooklyn with the same name, causing mail delivery delays. Apparently, anything with a Prospect Place address was routinely routed to Brooklyn, only to be re-routed. Hence the reason for the ballot.
The results of this referendum are lost to history; the street was eventually renamed Tudor City Place in 1947. More about that here.