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.