WASHINGTON (AP) _ Peggy Hare wants to buy replacement contact lenses from a discount mail- order house at half the price, but her optometrist refuses to give her a written copy of her prescription.

''The doctor would not let me get more contacts until I got an eye exam,'' she said

Because of her husband's recent bout with pneumonia, ''we are trying to pay off doctor bills' and can't afford $50 for another eye examination plus $87.50 for a new three-month supply of disposable lenses, Mrs. Hare said.

The mail-order house offered to sell her a supply for half the cost of her optometrist would have charged, said Mrs. Hare, of Hilliard, Fla.

''I have to keep wearing this pair until I get some money,'' she said.

Mrs. Hare says the optometrist refuses to release her prescription even though Florida is one of 15 states that require optometrists to give patients copies of valid contact-lens prescriptions.

Mrs. Hare says her prescripton is only a year old and under Florida law it is valid for another year.

But operators of mail-order houses that have sprung up in the last decade to offer discount prices of up to 50 percent off say that Mrs. Hare's experience is all too common.

''Prior to the advent of the mail-order houses, fitters had a monopoly, they controlled price, inventory. Once mail order came along, we offered an alternative to consumers,'' said Russ St. Cook, manager of Dial A Contact, of La Jolla, Calif.

The operators of mail-order companies charge that contact lens manufacturers, optometrists and ophthalmologists have used unfair tactics to curb the growth of this discount business.

They charge that large contact-lense manufacturers such as Vistakon, Bausch & Lomb and CIBA Vision Optics restrict sales to mail-order houses because of pressure from optometrists.

''The manufacturers are simply getting pressure from eye doctors who have a serious amount of market control'' because they determine what brands they will prescribe, said Monte Belote, director of the Florida Consumer Action Network, which complained to state authorities.

The Florida attorney general's office and the Federal Trade Commission are conducting separate inquiries into the contact-lense industry to determine if there are any antitrust violations.

The FTC declines to comment but industry officials acknowledge the agency is gathering information about sales and marketing practices.

Jerome Hoffman, antitrust chief for the Florida attorney general's office, said the investigation is trying to determine if ''there was any organized effort by the eye-care professional community to force the manufacturers to change their positions with respect to distribution.''

D. Biard MacGuineas, a Washington lawyer who represents the American Optometric Association, said the rapid growth of mail-order sales shows there is no restraint of trade.

Vistakon, CIBA Vision and Bausch & Lomb all say they sell their lenses to authorized fitters to ensure that patients receive correct prescriptions.

''It's primarily a health issue,'' said Harold Johnson, president of Bausch & Lomb's contact lens division.

Because its policy dates back to 1971, Bausch & Lomb says it couldn't have been adopted against mail-order houses in response to pressure from eye-care professionals.

But Lens Express President Brian O'Neill said the large manufacturers only began enforcing restrictive distribution rules in the last several years.

''I can show you invoices made out to Lens Express ... when we had open accounts with all these companies,'' O'Neill said. ''What their actual policies are and when they started taking an active stance with it are two very significantly different matters.''

In the meantime, Lens Express is fighting a lawsuit filed by the Texas attorney general that accuses the company of false advertising by failing to state that consumers need a prescription to order contact lenses.

O'Neill says the company contends that the lawsuit was filed in response to pressure from the state's optometry board. Lens Express also contends that Texas cannot control the content of national advertising on television and in magazines.

The 15 states, according to O'Neill, that require optometrists to furnish consumer with a written prescription are Alabama, Arizona, Colorado, Delaware, Florida, Maine, Nevada, New Jersey, New York, North Carolina, Ohio, Oregon, South Dakota, Vermont and Virginia.