Flag Etiquette
"When flown with flags of states, communities, or societies on separate flag poles which are of the same height and in a straight line, the flag of the United States is always placed in the position of honor - to its own right.
..The other flags may be smaller but none may be larger.
..
No other flag ever should be placed above it.
..The flag of the United States is always the first flag raised and the last to be lowered."
So, in other words, when state and federal flags are in a group, the state flag is lowered to half-staff whenever the federal flag is at half-staff. When it is by itself, the standards for flying the state flag at half-staff are dictated by the state.