A widely watched index shows home prices fell at the sharpest rate ever in the first quarter. The Standard & Poor’s/Case-Shiller National Home Price index released today reported home prices tumbled by 19.1 percent in the first quarter, the most in its 21-year history. Home prices in the New York area fell 11.9 percent. In the New York area, which includes parts of New Jersey, prices are back to where they were in June 2004. Home prices have fallen 32.2 percent since peaking in the second quarter of 2006 and are at levels not seen since the end of 2002. The 20-city index fell by 18.7 percent in March from the year before and the 10-city index lost 18.6 percent. But the rate of decline for both indexes slowed for the second month in a row. The New York-area data includes information from Bergen, Essex, Hudson, Hunterdon, Mercer, Middlesex, Monmouth, Morris, Ocean, Passaic, Somerset, Sussex, Union and Warren counties in New Jersey. Ap.