Billing it as a "once-in-a-lifetime opportunity," Maryland this week launched its long-awaited tax amnesty program, promising delinquent taxpayers who come forward that they may pay their debts without fear of financial penalties or criminal prosecution.

Officials, including Gov. William Donald Schaefer and Comptroller Louis L. Goldstein, staged a series of promotional press conferences across the state, including Silver Spring, urging compliance during the Sept. 1 through Oct. 31 amnesty period. They said the state hopes to recoup at least $20 million in unpaid personal, corporate, sales and other taxes.

Amnesty "is simple . . . and it is fair," Goldstein said Tuesday in Baltimore .

But, Schaefer warned, if any delinquent taxpayers fail to come forward "we're going to come after you."

Officials noted that much of the delinquent tax problem in Maryland is concentrated in Montgomery County, where a large transient population of Washington-based federal government employes, political appointees and private lobbyists live for brief periods before moving back to their home states. The officials said that many attempt to avoid paying Maryland taxes while living in the county.

For those who don't come forward during the amnesty period, the chances of getting caught afterward are greater and the consequences tougher, Goldstein said. The comptroller's enforcement office has been beefed up with additional audit and criminal investigation personnel, he said.

Penalties on outstanding income taxes will increase from 10 to 25 percent, he said, and criminal sentences for amnesty-eligible taxpayers will jump from one to five years' imprisonment and $1,000 to $5,000 in fines for each violation.

Although the state hopes to recover at least $20 million through the program, officials said it is impossible to estimate how many delinquent taxpayers there are in the state or how much they owe.

Modeled on recent amnesty programs in more than 20 other states, the Maryland initiative grew out of legislation enacted earlier this year by the General Assembly that would apply to taxpayers who owe any taxes that were due before last Dec. 31.

Goldstein cautioned that unpaid 1986 personal income taxes do not come under the program since the payment deadline for them is April 15, 1987. "The same goes for sales taxes collected in December 1986, but due in January 1987," he said.

Payable taxes under the program include personal and corporate income taxes, employer withholding taxes, retail sales and use taxes, admissions and amusement taxes and boat excise taxes.

Taxpayers are eligible for amnesty if they filed no returns, filed returns for deficient amounts or received a bill from the state for unpaid taxes, officials said. Any taxpayer currently under state investigation is ineligible.

Under the amnesty program, new prosecutions and unpaid civil penalties would be barred, but taxpayers still would have to pay accumulated interest on delinquent taxes.

Taxpayers will be able to pay delinquent amounts by check, money order or credit card, due by Oct. 31.

Initial efforts to publicize the amnesty program this summer got off to a rocky start when information fliers depicting Chicago gangster Al Capone as a tax evader drew complaints from leaders of the Italian-American community in Baltimore.

The fliers were withdrawn and replaced by another depicting Lt. Col. George Armstrong Custer, leader of a U.S. cavalry unit annihilated by Sioux Indians in a battle on the Little Bighorn River in Montana in 1876. A caption on the flier reads: "Custer was sure to beat the Indians. Are you sure you can beat Maryland out of back taxes?"

Officials have distributed special tax amnesty payment forms throughout the state. They are available at more than 1,200 banks, 230 libraries, 85 Giant Food stores and at all 15 comptroller branch offices in the state and at the offices of the clerks of the circuit courts for all 23 counties and the City of Baltimore. In addition, special boat excise tax forms are available at the five branch offices of the state Department of Natural Resources.

Tax experts also will be available on special telephone lines set up to provide information and other assistance. The main number is 1-800-MDTAXES, along with a separate Department of Natural Resources number, 1-800-492-1138, for boat excise tax information. TAX AMNESTY INFORMATION

Tax amnesty information can be obtained from the following Maryland Comptroller branch offices:

Montgomery County: Wheaton Plaza North Office Bldg., Suite LL6, 2730 University Blvd. West, Wheaton, Md. 20902. Telephone: 949-6030 or 949-6032.

Prince George's County: Metro-Plex I, Suite 450, 8401 Corporate Dr., Landover, Md. 20785. Telephone: 568-0222.

Howard County: State Multiservice Center, 3451 Court House Dr., Room 1067, Ellicott City, Md. 21043. Telephone: 461-0170.

Statewide: Two toll-free numbers are available. Call 1-800-MDTAXES for general information and 1-800-492-1138 for boat excise tax information.