The House Armed Services Committee and Army Secretary Clifford L. Alexander are in a skirmish that threatens to escalate to a full-blown congressional inquiry into the state of the Army.

It started when the committee concluded last week that Alexander was defying its repeated requests to make the case personally for reprogramming $14.6 million in fiscal 1980 money to beef up Army recruiting.

The committee not only denied the reprogramming request but also followed up with a letter demanding that Alexander appear as the leadoff witness in a broad investigation of today's all-voluteer Army, including recruiting problems.

The committee wants to know among other things, why the Army is signing up so few high school graduates these days.

Army recruiting figures show that only 37.3 percent of those admitted from Oct. 1, 1979, through May 19, 1980, were high school graduates. That is down from 52.2 percent in the like period a year earlier.

Alexender, in a telephone interview, confirmed that Chairman Melvin Price (D-III.) of the House Armed Services Committee wrote him on Thursday about the committee's intention to investigate the Army.

"I want to find out what it's all about. I've asked for a meeting with Chairman Price," said Alexander. "If it's about recruiting shortfalls, we're at 100 percent" of the objective for volunteers so far in fiscal 1980.

"The genesis of all this came from some strange ramblings of Robin Beard," Alexander said. "When he opens his mouth, you never know what is going to come out."

Rep. Beard of Tennessee, a Republican member of the House Armed Services Committee, has been firing away at Alexander and Defense Secretary Harold Brown for months, claiming they are trying to cover up the sad state of the American military.

During Wednesday's debate on the Pentagon procurement bill, for example, Beard complained that "one of the most critical problems we still have is a secretary of the Army running around saying we have the best quality Army ever, totally misrepresenting the facts to the American people.

"Yet all the statistics," Beard continued, "indicate a critical situation at this time. We need to find out."

Army officials conceded they are vulnerable statistically in some areas, including the declining percentage of high school graduates.

However, they said, the Army-unlike the other services-has made the policy decision to fill up the foxholes with nonhigh school graduates, if necessary, rather than go short.

By contrast, Marine leaders have decided to reduce the size of the corps if they find they cannot achieve their goal of 75 percent high school graduates among volunteers.

"It's a judgment call," said an Army planner.

Another controversial statistic is the number of people the Army is taking in who rank in the lowest acceptable mental category in the entrance tests. About 10 percent of Army enlistees rank in this category. The number is on the rise this year.

Another trend worrisome to some critics of the All Volunteer Force is the proportion of blacks, especially in combat units. About 35 percent of the male Army volunteers continue to be black, and they are more inclined to reenlist than whites.

If the House Armed services Committee inquiry goes forward as planned, Alexander would be called to testify in mid-june. The committee would later conduct hearings at or near bases to get first-hand testimony about the quality of today's Army.

This would be the committee's first full-scale probe into the state of the all-volunteer Army.