The growth in personal income slowed sharply in April, the Commerce Department reported yesterday, providing another indication that economic growth tapered last month.

Personnal income grew $6 billion to a seasonally adjusted annual rate of $1,861.8 billion in April, compared to a $14.3 billion increase in February and a $22.5 billion jump in March.

As with other April statistics, the gain in personal incomes was held down by the effects of the Teamsters strike, but apart from that, increases were still modest, analysts said.

Also reflecting the strike impact, capacity utilization in manufacturing fell from the relatively high 86.1 percent rate in March to 84.9 percent last month, the Federal Reserve Board said.

Capacity utilization figures compare the actual use of production facilities with what manufacturers, basis materials producers and utilities theoretically could turn out at full production.

But just as not all of the 1 percent drop in industrial production in April reported this week by the Fed was due to the strike, part of the decline in capacity utilization was due to other factors.

The trucking strike, resulting lay-offs in manufacturing, and the United Airline strike by mechanics combined to reduce wages and salaries about $5.5 billion below what they otherwise would have been. Widespread flooding in the South cut construction wages and salaries by about $1 billion.

Overall, private wages and salaries were up only $1.5 billion from March to April, compared to a $14.9 billion increase from February to March. Adding in the $6.5 billion effect of the strikes and weather still leaves an April gain only about half as large as the month before.

Non-wage income rose $3.6 billion in April, compared to $7.8 billion in March. Transfer payments, such as Social Security or private pension benefits, increased $1.3 billion compared to $3.3 billion the month before.

Rental income dropped $0.9 billion compared to a $0.2 increase in March.

Jack Carlson, chief economist for the U.S. Chamber of Commerce, said that the recent economic statistic, taken together, indicate that a slow-down in economic activity began in April.

"The $6 billion increase in personal income fell two-thirds short of making up the income lost during April to inflation," Carlson said. "If additional evidence of slower economic growth should appear in the weeks ahead, the prospect for decelerating the country's double-digit inflation will improve," he added.

Prior to the drop last month, capacity utilization in manufacturing had been running only about two percentage points below the peak levels of 1973. A shortage of capacity in some industries, including basic metals, has been blamed by Carter administration economists for some of the rapid rise in prices in the industrial sector.