SYDNEY (Reuters) - Several lawmakers filed family history documents in Australia s parliament to meet a government deadline on Tuesday to try to prove their citizenship and stem a crisis that has so far claimed nine MPs and cost the government its majority.     Australia s 116-year-old constitution bans dual citizens from holding national office and the High Court adopted a strict interpretation of it in October in a country where half the population were either born overseas or have a parent who was. The crisis may yet plunge Prime Minister Malcolm Turnbull s Liberal-National coalition into minority rule, should it lose another lawmaker, or a crucial by-election set for Dec. 19.      The ruling center-right pairing lost its one-seat lower-house majority when the High Court found Deputy Prime Minister Barnaby Joyce to be a New Zealander and therefore ineligible for office. He has since rescinded his New Zealand citizenship and regained his seat in parliament.   But another member has since quit his place and now as many as a dozen more now face referral to the court after the deadline to disclose the birthplace of parents and grandparents passed on Tuesday. The disclosures show that nearly every lawmaker has at least one foreign parent or grandparent. While some provide citizenship records dating back to the 19th century, others give few details or documents, prompting calls for the High Court to consider their cases.      There are a few grey areas, there s no doubt about that,  MP Christopher Pyne said on Perth radio station 6PR, adding that parliament would decide on Thursday which cases to send to the court. One opposition Labor Party member has already told parliament it  remains unclear  whether he is British, after the Home Office could not find the paperwork to prove he renounced his citizenship a decade ago. Labor argues that seven government lawmakers filed  unconvincing  or  incomplete  disclosures, while the government raised doubts over four opposition MPs, and there is a cloud over another independent lawmaker. Although Joyce easily regained his seat at a by-election on Saturday, the crisis still has the government precariously clinging to power and has already dented its ability to pursue its political agenda. If it loses a by-election in Sydney on Dec. 19, or the court ousts another lower-house MP, it would be forced to depend on a handful of independent lawmakers to retain power and pass laws. 