U.S. builders began work on fewer homes in March after they sharply reduced apartment construction, but builders requested the most permits for future projects in more than three years, suggesting many anticipate the housing market could improve over the next year, the government reported Tuesday. The Commerce Department said housing starts fell 5.8 percent last month to an annual rate of 654,000 units. It was the biggest percentage drop since April 2011, though most of the drop was in the volatile multi-unit category, which plunged 16.9 percent. Starts for single-family homes fell 0.2 percent. Permits, a gauge of future construction, rose 4.5 percent to an annual pace of 747,000, the highest since September 2008. The long-distressed housing sector has showed signs of a nascent recovery in recent months, and homebuilding could add to economic growth this year for the first time since 2005. Still, an oversupply of unsold homes, which is depressing prices, remains a major obstacle to recovery in the sector.