Although a normal hospital birth now costs an average of $3,200, about one-quarter of all the nation's women in the prime childbearing years have no health insurance to pay the bill, according to a study released yesterday by the Alan Guttmacher Institute.

The nonprofit organization, which researches birth and family-planning issues, said that calculations derived from recent Census Bureau findings show that a quarter of all women 18 to 24 lack health insurance or government health services under such programs as Medicaid. Fifteen percent of women in the next major childbearing age group, 25 to 29, also are without coverage. These two age groups account for about three-quarters of all U.S. births.

Most of those without coverage have low incomes. If all low-income women of childbearing age, 15 to 44, are taken into account, about one-third with family incomes below $15,000 last year had no health insurance.

The Guttmacher study, written by Rachel Benson Gold and Asta Kenney, said 95 percent of all U.S. births occur in hospitals, raising the question of who pays the big bills when so many women lack insurance.

Although some of the women without coverage pay the costs out of pocket, in many cases they are taken as charity patients or they simply run up a bill and never pay it. As a result, the hospital and doctor get stuck with unpaid bills and either absorb the losses, shift costs to other patients who have insurance or try to get aid from local health agencies.

A recent study by Vanderbilt University researchers, the Guttmacher study said, concluded that births are responsible for about 37 percent of all admissions in which the hospitals are not compensated or are paid directly out of the patient's pocket.

In addition, hospitals bear the costs of caring for newborns in many cases; Vanderbilt Hospital estimated that 27 percent of all its uncompensated costs were for newborns.

Nationwide, it has been estimated that hospitals provide $6.2 billion a year in uncompensated care for all types of cases -- a major financial burden, especially for inner-city and public hospitals.

The Guttmacher study said that although the federal-state Medicaid program was intended to provide coverage to low-income women, there are large coverage gaps because states set their own standards. Half of obstetrician-gynecologists do not participate in Medicaid, which often offers only small payments to doctors. In addition, some private health policies do not cover maternity care.

According to the recommendations of the American College of Obstetricians and Gynecologists, a pregnant woman should have at least 13 prenatal visits, beginning very early in the pregnancy. In addition to the cost of those visits, the study said, typical costs of a normal birth are likely to total more than $3,200, and for a Caesarean delivery about $5,000.

Despite doctors' recommendations for early prenatal care, another study published by the Guttmacher Institute yesterday estimated that three-quarters of all pregnant women (two-thirds of blacks and low-income women) received care in the first three months of pregnancy during 1980. Eighteen percent received no care until the second three months, and 5 percent received care in the last three months or not at all.