After rejecting more liberal rules for state-funded abortions last week, the General Assembly is now faced with another controversial measure that would require girls under 17 to have parental or judicial consent before getting an abortion.

The bill, sponsored by Sen. William H. Amoss (D-Harford) and Del. Patrick C. Scannello (D-Baltimore), is modeled on a Massachussetts law and has been endorsed at the federal level by some members of Congress and officials in the Reagan administration. Three years ago, however, the U.S. Supreme Court ruled that states cannot require the notification of parents or their consent in instances of teens seeking abortions.

Maryland is one of four states that now require parents to be notified--although not to give their consent--but the law is flexible enough to enable doctors to perform abortions without parental notification in some circumstances.

The Maryland bill, which evoked emotional testimony at House and Senate hearings this week, would exempt girls who get a judge's approval for an abortion.

The measure originally was believed to have little chance of passing either the Senate or the House committees, but some legislators who favor giving women the choice fear that last week's vote against broadening the scope of state-funded abortions may add momentum to anti-abortion forces in both chambers.

In testifying for his bill, Scannello said: "Slowly but ever so surely the family, as we know it, is being shattered beyond repair. We've got to preserve the family as a functional and durable unit in society and preserve the authority of parents over their children."

Olga Fairfax, representing Methodists for Life, called abortion "a quick dirty fix" that has led to the disintegration of the family and a host of pyschological problems for family members.

Another supporter of the bill, a mother from Harford County, said her 16-year-old daughter had been able to get an abortion without her consent and that medical complications ensued.

"We want complete control over their lives . . . ," the woman told members of the House Committee on Environmental Matters. "Parents have rights too."

But Del. Paula Hollinger (D-Baltimore County) shot back: "Did this child, who was obviously having sexual relations, have the freedom to communicate with you about contraception that could have prevented the need for the abortion in the first place? In your household was there that kind of communication? Where was the failure in your household?"

Representatives of Planned Parenthood and other opponents of the bill said the consent requirement could jeopardize the health of some desperate, pregnant teen-agers who delay getting abortions until they are medically risky because they fear abuse from their parents.

According to an official from Marylanders for the Right to Choose, a 1980 study conducted by the Alan Guttmacher Institute showed that 76 percent of teen-age women surveyed said they would inform their parents of their decision to get an abortion. But the remainder said they would not, even if it were required by law, and some said they would risk having illegal abortions or would run away from home.

Planned Parenthood officials said that of 281 teen-agers under 17 who sought abortions in their clinics in Maryland last year, 133 were accompanied by parents and 52 told their parents. The rest either said they feared retaliation by their parents or were from broken homes. About 5,600 Maryland teen-agers had abortions in 1980, according to the study.

"I absolutely cannot imagine passage of this bill will help any family in crisis," said Rosalie Streett of the Maryland State Committee on Adolescent Pregnancy. "If they had not been able to communicate before the young girl became pregnant . . . is this bill the magic cure to family communication?"