What are the spectroscopic signatures that differentiate triple state water from water at 1 atm? According to the Wikipedia article Triple point of water, the triple point of water occurs at


  The single combination of pressure and temperature at which liquid water, solid ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C; 32.02 °F) and a partial vapor pressure of 611.657 pascals (6.11657 mbar; 0.00603659 atm).


Shown in the illustration below (from the Wikipedia article):



Crucially, to put this into a context, the 611.73 pascals quoted in the article corresponds to the 


  minimum pressure at which liquid water can exist. At pressures below the triple point (as in outer space), solid ice when heated at constant pressure is converted directly into water vapor in a process known as sublimation.


Potentially useful information to determine if an exoplanet can possibly have water (if all other conditions are suitable).

What are the spectroscopic signatures that differentiate triple state water from water at 1 atm?
The triple point of water is point of dynamic equilibrium between three phases of water. Any small change in Pressure or Temperature will lead to one phase regions or two phase lines on the phase diagram. 

The triple point is not a state of matter rather a combination/mixture of three phases . So i very much doubt we can get any unique spectroscopic signatures . We would get a distorted result as this point has three different phases. 
Also Emission and Absorption spectra depends on  temperature and pressure.