My cousin and I were talking about this and we could not come to a conclusion. Obviously it is very hard to keep cryogenic propellants at a liquid with the temperatures involved, but if they pressurized them purposefully then when they exited into the combustion chamber they would become a gas unless the pressures were also kept high enough. Does it come out as a liquid or a gas and is it held at a liquid because it’s pressurized or cooled?
It's possible to inject in either state, but far more common to inject as liquid state so that one can design the oxidizer and fuel streams to intersect each other, creating a large splash fan where the propellants can mix well together. This is usually accomplished by pumping the cryogenic components and raising their pressures from the relatively low pressure in the tanks, thus keeping them liquid as they pass through the injectors. The exceptions are the cases where a cryogenic propellant is used to regeneratively cool the engine and thus picks up too much heat to stay liquid. Sometimes the gas is then injected at the perimeter of the engine to act as a film of relatively cool gas that doesn't completely burn and thus protects the wall, or it's diverted to a vernier engine for thrust vectoring, or it's mixed in elsewhere in combination with the rest of the liquid propellants. Some hybrid rocket designs which use LOX actually prefer a gas injection state since in a hybrid system mixing happens in the gas state at the boundary layer where the solid propellant gas evolves from the receding solid surface.