Michigan corrections officials yesterday gave Gov. James J. Blanchard a letter that will trigger the early release of 500 prisoners, who will join about 14,000 other ex-convicts across the country whose sentences have been cut short in the past three years because of overcrowded prisons.

South Carolina became the latest state to use this safety valve yesterday as it released the first of 330 prisoners to make room for new inmates. At least 10 other states have adopted emergency early release programs since 1980, and seven have turned prisoners loose in the last year.

State officials admit that some of the convicts are committing new crimes during their early release periods, but they say they cannot afford to build enough new prisons to keep up with the growing inmate population.

"The emergency has become business as usual," said Bill Kime, deputy director of Michigan's corrections department, which declared the state's prisons to be full beyond capacity for the sixth time in two years. Michigan already has released nearly 2,000 prisoners as much as a year and a half early.

But such efforts have stirred bitter controversy in Illinois, where the courts struck down an early release program in July after local prosecutors argued that rapists and other violent offenders were being freed and committing new crimes.

Since the late 1970s, a spate of mandatory sentencing laws, rising crime rates and more arrests, coupled with stiff public resistance to the burgeoning cost of prison construction, have pushed the overcrowding problem to crisis proportions. At least 22 states and the District of Columbia are now under court order to ease prison congestion.

At the end of last year, the United States had a record 412,303 people behind bars, more than the population of Miami. The 1982 increase of 42,915 was the largest since the government began counting in 1925. Most of the convicts are in state prisons.

Michigan's legislature, seeking to avoid a court order, passed a law requiring the governor to declare an emergency whenever the system's capacity of 13,047 is exceeded for 30 consecutive days, as happened yesterday. Enough prisoners must be released to lower the population to 95 percent of capacity.

The key is the law's mandatory feature, Kime said, because "It takes the political heat off your elected officials . . . . It faces people with the right choice: either build more prisons or live within your capacity," Kime said.

But, he added, "Eventually you'll scrape the bottom of the barrel of people you can let out."

On five previous occasions the law has forced Michigan to reduce most prisoners' sentences by 90 days, except those convicted of such offenses as murder, rape and kidnaping. The 90-day reductions accumulate for prisoners who are not released, so that an inmate sentenced to five years before early 1981 now must serve only 3 1/2 years.

Jim Boyd, director of a Michigan prison reform group, said the problem was exacerbated by such measures as a two-year minimum sentence for anyone caught using a gun during a felony. Increasingly crowded conditions led to serious riots that rocked three large institutions in 1981, he said.

"People don't like this law," Boyd said, "but it hasn't confirmed the worst fears that opponents tried to play upon when it was passed."

A 1981 study found 117 serious felony arrests among the 2,000 or so new parolees during their period of early release.

"It wasn't a crime wave," Kime said, "but there were 117 victims, including one or two homicides."

In Illinois, where angry prosecutors challenged the program in court, 10,019 convicts have been released early since 1980, only to have their beds quickly filled in the 14,000-cell system.

Aides to Gov. James R. Thompson were making liberal use of a provision for cutting prison sentences for good behavior, granting "good time" in blocks of three to nine months instead of a day at a time.

"For long periods of time, rapists and other serious offenders were getting out early," said John Barra, state's attorney for Peoria County. "Every Friday they'd release as many as were sentenced that week."

Barra said one man, convicted of resisting arrest, murdered his wife soon after his early release.

"We've had quite a few burglars as soon as they got back out, they committed another one," he said. "As long as you keep letting them out the back door, we're not going to solve the problem."

Meanwhile, Illinois officials contracted to send 20 inmates to Nevada institutions, and last week they moved 25 onto mattresses on the floor of a Hillsboro chapel. Such measures are not unusual. Oklahoma has converted several motels to minimum security prisons, while Wisconsin has shipped 200 inmates to Minnesota.

Jack Stoddard, a Wisconsin prison official who has granted early release to 700 inmates, said the program works in his state because violent offenders are screened out and newly freed inmates are supervised closely by parole officers. He said the state has reaped substantial savings by cutting out 38,396 prison days.

South Carolina's law, adopted in July, automatically triggered yesterday's release, although the governor has the power to overrule such an order.

"The alternative is to continue to operate at 140 percent of capacity," said Deputy Corrections Commissioner Hugh Clements.

In Mississippi, where officials have wide discretion in granting early parole, 1,119 offenders destined for state prisons are backed up in county jails. Other states that have adopted early release programs are Alabama, Arizona, Missouri, New Jersey, Washington, Utah and Iowa.