NEW YORK, June 20 (Reuters) - Applications to buy and refinance homes dropped last week, an industry trade group said on Wednesday, the latest sign that U.S. housing remains mired in a downturn.

The Mortgage Bankers Association's mortgage application index slid 3.4 percent to a seasonally adjusted 643.7 in the week ended June 15.

Thirty-year mortgage interest rates dipped 0.01 percentage point last week to 6.60 percent, the MBA said.

The MBA's seasonally adjusted purchase index fell 3.0 percent to 450.9 while its refinancing applications index shed 4.2 percent to 1,776.8 on a seasonally adjusted basis.

The drop in applications piled on to reports from the country's builders and the government this week suggesting any sustained housing rebound could be next year's business.