The Senate President Stephen Parry emailed Senators to say that after receiving Mr Day's resignation, he had to write to the South Australian Governor to say he was not sure it created a casual vacancy for which Family First could nominate a replacement.
The Attorney-General George Brandis and Special Minister of State Scott Ryan then released a statement confirming that government is referring the matter to the High Court for resolution.
The statement said that it relates to section 44 of the Constitution, regarding a potential indirect pecuniary interest in a contract with the Commonwealth.
SBS News understands it may relate to arrangements around Mr Day's electoral office.
