The number of families with more than one bread-winner declined sharply in the year ending June 30, reflecting a tightening job market, the government said in a report released yesterday.

The Bureau of Labor Statistics, surveying the "usual weekly earnings" of individuals and families from the third quarter of 1981 through the second quarter of this year, said the number of multi-earner families plunged by nearly 600,000 -- to 21.2 million.

But despite the increasing scarcity of jobs, about 56 percent of all married couples still had more than one member of the family working during the year ending last June 30, the report said. Only 29 percent of the families headed by women had more than one wage-earner in the household.

Meanwhile, new government figures yesterday indicted that U.S. business inventories rose 0.3 percent in June, the second spurt of growth in seven months, as slow sales in showrooms kept unsold goods waiting in warehouses and on company back lots.

Business inventories were up $1.7 billion to $512.1 billion, after adjustment for seasonal trends, the Commerce Department said. The value of inventories in May had dropped by a revised 0.9 percent.

The value of goods yet unsold is reported with a considerable lag by the government but is closely watched by economists for signs that warehoused stocks are finally as low as they can get. Until inventories require rebuilding, businesses tend to postpone the increases in production that signal an economic turnaround.

The inventory-to-sales ratio for June showed 1.49 months' worth of supply on hand at June's rate of sales, less than April's ratio of 1.52 but more than May's 1.46, the department said.

Sales dropped 1.3 percent in June to $344.5 billion, with durable sales leading the way down with a 2.6 percent decline, mostly in automobiles.

Retail inventories were up 1.65 percent in June, the department said.