A mezuzah is placed on the right doorpost of the one entering the room or building.
An emergency exit is not entered from the outside and is only used as an exit -- typically to a unenclosed open area. Does it require a mezuzah? If it does, where is the mezuzah placed?
The location of a mezuzah of an enclosed deck is subject to dispute, as discussed here. However, the location of a mezuzah on a unenclosed deck door is on the right going into the house since the deck is treated as the outside and not a room of the house. An emergency exit may be completely exempt since it is not used as an entrance at all.