Nancy Reagan made another excursion into the medical world yesterday, and Children's Hospital officials, taking full advantage of their captive audience, pleaded for help in soliciting private-sector money.

The first lady was invited by Dr. Catherine Hammock, chief of neurosurgery, to visit the new Brain Research Center devised to study and treat the neurological problems of infants and children. It was Mrs. Reagan's second visit to the hospital.

"Unless we move to private support soon, we're heading for disaster," Dr. Karl Knigge, chairman of the department of neurology at the University of Rochester, told Mrs. Reagan. "Forty percent of time in neurological research is being spent on federal paperwork, and it is endangering the imagination of new, young people, forcing them not to be unique and experimental . . . With your kind of support, we can take the lead in experiments."

"Are you saying that the old way results in too much time being spent on paperwork instead of being able to do work?" asked Mrs. Reagan. "And that you'd rather not have intrusion of the government so you can do work?"

"It's not the intrusion of the government," demurred Knigge. "I don't want to get into a political discussion."

"Nor do I," said Mrs. Reagan.

"With private funds, research can be uninterrupted," he continued. "Government contracts limit the time spent, so that there is no real commitment from doctors. They are pressured for results. With private funding, the pressure comes from within. We can be more creative."

Nancy Reagan, appearing relaxed and self-assured, began her hospital tour in a playroom for children with neurological problems ranging from spinal disorders to brain tumors. The 10 or so toddlers, some in head bandages and body braces, were a touching sight. Hugs and kisses between the children and their visitors abounded.

"I'm drawing this for Mrs. Reagan," offered 3-year-old E.G. Williams, scribbling in crayon on paper.

"Mine's for you, too," piped up Beth Gurney.

"I'm going to show them to my husband, and we'll hang them on the wall," Mrs. Reagan said.

Next, she was escorted to the research center, several rooms with some elaborate computers. "I used to go to Northwestern University where my father was a professor of neurosurgery there and and watch him cut a brain," remembered Mrs. Reagan. "I was so fascinated by it all. But this is all certainly different from what I watched my father do."

Among other things, she was told the computers can determine the effects of various drugs on the brain. "Can you test the effect of pot and cocaine and so on?" inquired Mrs. Reagan, raising her interest in drug abuse. "It seems to me if you could show young people who don't believe drugs are problem . . . It's very serious."

Later Mrs. Reagan asked how long it would take to determine the effects of popular drugs on the brain. The doctors agreed it would take about six months, and that they would ultimately need a "dramatic way"--such as the White House's public backing--to let young people know the dangers.