Are “Turn Around Don’t Drown” signs allowed in New York State?

No, the sign is not in the MUTCD and does not provide a clear message. If the water is deep enough, the road should be closed. The use of a text message sign that is not in the MUTCD requires approval from NYSDOT. Only minor modifications of standard signs can be used without special permission, as per Section 1A.03 in the NYS Supplement.

Text from MUTCD (Combination of the National MUTCD and NYS Supplement)

Section 2C.35 Weather Condition Signs
(W8-18, W8-19, W8-21, and W8-22)

Option
The ROAD MAY FLOOD (W8-18) sign may be used, as necessary, to warn of a roadway section which remains passable, but is covered by water which requires greatly reduced travel speed and/or obscures a significant length of pavement.

Guidance
The ROAD MAY FLOOD sign should be used only where the roadway remains, or is expected to remain, passable during its flooded condition. Where a roadway is, or is expected to become, impassable, it should be closed and suitably posted with ROAD CLOSED (R11-2) signs .

Option
A Depth Gauge (W8-19) sign may also be installed within a roadway section that frequently floods.

Standard
If used, the Depth Gauge sign shall be in addition to the ROAD MAY FLOOD sign and shall indicate the depth of the water at the deepest point on the roadway.