The Indian Rupee continued to fall against the American currency, declining by 37 paise in late morning trade on monday to 62.60 per dollar on persistent dollar demand from banks and month-end buying from importers coupled with higher dollar overseas.The rupee resumed lower at 62.55 per dollar as against the last closing level of 62.23 per dollar at the Interbank Foreign Exchange (Forex) Market and dropped further to quote at 62.60 per dollar at 1040hrs.It moved in a range of 62.34-62.60 per dollar during morning deals.