Housing construction in the US posted a better-than-expected performance in March, rising to the highest level in 16 months on the strength of multi-family homes. But the Commerce Department report Friday showed that construction of single-family homes, the most important segment of the market, fell. It dropped 0.9 percent to an annual rate of 531,000 units, after a strong 5.7 percent gain in February. The sluggish nature of the housing recovery has helped slow the rebound of the broader economy. Overall, construction rose 1.6 percent to a seasonally adjusted annual rate of 626,000 last month. That was higher than the 610,000 level that economists had expected. In addition, the government revised February to show a 1.1 percent gain rather than the initially reported drop of 5.9 percent. Applications for building permits, considered a good barometer of future activity, also recorded a better-than-expected increase, rising 7.5 percent to an annual rate of 685,000. Analysts are looking for any rebound in housing to be modest at best given the severe problems still facing the industry. These include record home foreclosures and high unemployment, which robs potential buyers of the incomes they need to support a home purchase. The weakness in single-family construction was offset by an 18.8 percent surge in the smaller multifamily sector, which rose to a seasonally adjusted annual rate of 95,000 units.