The government published fresh figures yesterday showing a moderate decline in housing starts - the first firm sign of the long-expected tapering off in home construction in the face of the recent rise in mortgage interest rates.

New statistics compiled by the commerce Department showed overall starts down 4.9 percent in May, following steady increases during the first four months of the year. Although the dip came mostly in multi-family units, singlefamilu starts also declined.

At the same time, the department reported that the personal income of Americans rose a hefty 0.9 per cent in May - not quite as vigorous as the 1.3 percent jump recorded the previous month, but stell a respectable pace.

Separately, the Federal Reserve Board announced that, collectively, America's factories were operating at 83.6 per cent of their capacity last month, compared to 83.4 per cent in April - continuing the trend that has prevailed for the past several months.

The combination of figures appeared to suggest that recovery still is continuing at a relatively robust pace, despite recent predictions that a slowdown is likely later this year. The fall off in housing starts has been the first sign of any weakness.

William A. Cox the Commerce Department's deputy chief economist, said both the housing and personal income figures were in line with expectations. Most analysts are forecasting a strong second quarter before the slowing begins in the second half of the year.

The 4.9 per cent drop in housing starts still left total private starts at an annual rate of 2.075 million - high by historial standards. Single-family starts declined 0.8 per cent, while multi-family starts fell 13.8 per cent.

However, in a key indicator of future trends, the number of new building permits issued across the nation fell 8.8 per cent, to a new annual rate of 1,587 million units. Overall housing starts last mont were 4.7 per cent higher than their pace a year ago.

Jenneth M. Plants, vice president for research of the Federal Home Loan Mortgage Corporation, said the May decline in starts "indicates that the 1978 housing boom has peaked," He predicted starts would average 1.8 million to 1.9 million units in the third quarter.

The rise in personal income was buoyed by a sharp jump in farm income. Which soared 13.6 per cent in May. following a 3.2 per cent climb in April. The increase reflected higher prices for livestock and raw agricultural products.

Income from wages and salaries grew by 0.6 per cent over the month, following a 1.6 per cent increase in April. Factory payrolls were up 0.5 per cent, compared with an 0.7 per cent jump the previous month. Government benefits payments climbed 0.9 per cent, after falling before.

The increases brought overall personal income for the nation to a new annual rate of $1.693 trillion up $15.4 billion from April's pace. In March personal income rose 1.4 per cent, or $22.1 billion to an annual rate of $22.1 billion, to an annual rate of $1.657 trillion.