The board of the American International Group has declined to join a lawsuit against the federal government over its $182 billion taxpayer-financed bailout, the New York Times DealBook blog reported yesterday. The decision follows a public uproar over the possibility that AIG would sue the same authorities that rescued it during the financial crisis. The board had been weighing whether to join a $25 billion lawsuit filed by its former chief executive, Maurice R. Greenberg, on behalf of shareholders, arguing that they lost tens of billions of dollars when the government attached onerous terms to the bailout.