Earlier quoted context omitted.
It is state law. A municipality can't override it.
Do you have a state law reference that covers T intersections?
S 1202. Stopping, standing or parking prohibited in specified places.
1. Stop, stand or park a vehicle:
d. On a cross walk;
2. Stand or park a vehicle, whether occupied or not, except
momentarily to pick up or discharge a passenger or passengers:
b. Within twenty feet of a cross walk at an intersection, unless a
different distance is indicated by official signs, markings or parking
meters;
Formal definition of a crosswalk in Article 1: S 110. Crosswalk.
(a) That part of a roadway at an intersection included within the
connections of the lateral lines of the sidewalks on opposite sides of
the highway between the curbs or, in the absence of curbs, between
the edges of the traversable roadway.
(b) Any portion of a roadway at an intersection or elsewhere
distinctly indicated for pedestrian crossing by lines or other markings
on the surface.
In other words there are crosswalks at every intersection whether marked or not. Crosswalks elsewhere must be marked to be recognized as such. That is why the unmarked curb cuts in the middle of a block don't count for parking violations. T intersections are not special in any way and are subject to the same rules as all others.