District of Columbia police officials are quietly questioning the adequacy of protection provided by U.S. Park Police on Tuesday when militant Iranian Students broke through U.S. Park Police lines at the Ellipse and attacked pro-shah demonstrators, injuring scores of them.

The ripple of privately voiced criticism, rare among sister law enforcement agencies, apparently has occurred because D.C. Police had special riot-trained officers on standby in the area, but Park Police never requested their assistance.

The Ellipse, just south of the White House, is part of the national park system, and the 500-member Park Police force has initial jurisdiction over events there. Customarily in the past, they have requested assistance from the much larger D.C. police force in large-scale emergencies.

On Tuesday, a line of three-dozen horse-mounted park policemen and several footmen crumbled into disarray when hundreds of stick-wielding students rushed the pro-shah demonstrators just as Shah Mohammad Reza Pahlavi was being greeted at the nearby White House for his two-day state visit here.

Some Park Police reinforcements arrived.Tear gas was thrown, and a few minutes later police succeeded in separating the demonstrators.

The incident sparked criticism of the police by leaders of the pro-shah demonstrators and an apology by President Carter to the shah for the unpleasantness, which was visible from the White House.

Park Police Chief Jerry Wells said through a spokesman yesterday that the suddenness, intensity and ferocity of the student attack would have breached virtually any police line, no matter how strong.

Also, the spokesman said, the incident "was over so quickly that it hardly occured to (Wells) to ask for assistance."

Some D.C. Police officials have indicated that they feel there should have been a greater "show of force" before the incident started as a deterrent, similar to the shoulder-to-shoulder ranks of baton-carrying D.C. civil disturbance unit officers who marched against antiwar demonstrators in the 1960s.

Other D.C. officials said there were at least 170 riot-equipped officers of the D.C. Police Department's special operations division in the White House area, most of them on scooters and many available to give immediate emergency help.

A report drafted yesterday by Park Police for the National Park Service disputes this.

"The Metropolitan (D.C.) Police were transmitting radio messages which indicated that they were heavily engaged with 'anti' demonstrators in the 1500 block of E Street, 17th Street and Pennsylvania Avenue and 17th and G Streets," the report says.

D.C. Police officials contend that most of their officers were either idle (on standby) or engaged in relatively minor activity such as directing traffic.

The Park Police report says that about 150 park policeman were at the Ellipse before the major violence errupted at 10:35 a.m. At 10:23 a.m., the report said, when some preliminary rock and throwing by demonstrators occurred, an additional 56 reserve officers were rushed in by bus and car from a staging point near the Reflecting Pool.

Even with those reinforcements, Wells said yesterday through a spokesman, it was impossible to block the sudden attack of the Iranian students. More than 20 Park Police officers were injured in the melee.

The White House, State Department, Iranian Embassy and Park Police all deny recurrent rumors that the Carter administration had requested a "low profile" police presence at the Ellipse to avoid a police state atmosphere for the shah's ceremonial arrival.