Tailwheel's description is 99.9% correct. Just to add the final bit: there was a referendum in 1977, two years after the tumultuous events of 1975, and one of the questions addressed this matter of casual vacancies in the Senate and political allegiance. Prior to the referendum it was only traditional, not mandatory, that a replacement be of the same political party. Hence the 1975 events. The question put at the 1977 referendum proposed that it be mandatory for replacements to be of the same party. The question was passed in the affirmative so, yes, it is mandatory that the NSW State Parliament chooses an ALP replacement for Senator Arbib. Both lower and upper houses choose and vote.
I find it quite amusing and incredulous that the NSW Lib/Nat Coalition Govt is required to choose an ALP man to send to Canberra as Foreign Minister! You would think that they wouldn't necessarily simply endorse the PM's choice, or the choice of the "faceless men of Sussex St". You'd think they'd choose someone incompetent, with no real qualifications, someone destabilising, someone with a big ego, with leadership ambitions of his own perhaps, someone who might cause further problems for Gillard and the Govt.
WAIT A MINUTE.....