Q:

Is it possible that only one hemisphere of a planet has an atmosphere?

Suppose there is a tidally locked planet orbiting a star. The planet's surface consists of a global ocean, that is, liquid water. At the inner hemisphere the temperature is so high that the water is constantly boiling, creating the atmosphere of water vapor. But the vapor does not reach the dark side of the planet, and precipitates around the terminator line. The further side has no atmosphere and an icy surface.
Is this setup possible? Can it be such thing that one side of a planet has liquid (and boiling) water surface while the other side has no atmosphere?
Is it possible at all that a part of an ocean was boiling while the other one was icy?

A:

The atmosphere, if present on the daylight part of the surface, will be also present in the night side, providing mechanisms for heat transport from day side to night side. So if daylight side allows liquid water, the night side will be not much colder than cold places on Earth. 
Have a look at a paper:

Merlis, T. M., & Schneider, T. (2010). Atmospheric Dynamics of Earth‐Like Tidally Locked Aquaplanets. Journal of Advances in Modeling Earth Systems, 2(12). online pdf

From the abstract:

Free-atmospheric horizontal temperature variations in the slowly rotating atmosphere are generally weaker than in the rapidly rotating atmosphere. Interestingly, the surface temperature on the night side of the planets does not fall below, $240\,\text{K}$ in either the rapidly or slowly rotating atmosphere; that is, heat transport from the day side to the night side of the planets efficiently reduces temperature contrasts in either case. 

