THE JUSTICE Department now concludes, after an extensive investigation, that there are no grounds for appointing a special prosecutor in the Allen case. But as the president's national security adviser, Richard V. Allen is required to meet a higher standard than the common criminal laws.

The Justice Department has answered one extremely important question; it has arrived at an authoritative finding that Mr. Allen did nothing illegal. But only Mr. Reagan himself can answer the next question: whether Mr. Allen did anything improper, as Mr. Reagan defines that term for the people to whom he has given very great responsibilities.

It all goes back, of course, to the famous envelope with the $1,000 in it, and the wristwatches that Mr. Allen took from a Japanese magazine writer. Regarding the money, the Justice Department announced three weeks ago that there was no reason to doubt Mr. Allen's explanation that he intended to turn the money over to the Treasury. The FBI found that he had mentioned the envelope to other people, and had left it in a safe to which others had access--hardly the conduct of a person who meant to keep the money for himself. As for the watches, Allen kept them, but here again the department finds no evidence that the law was violated.

That makes Mr. Reagan's decision harder, for now he must apply his own rule of personal conduct --always a less explicit measure than the law. It seems absurd, at first glance, that a man entrusted with the central life-and-death issues of the country's security should be weighed by a trivial incident involving wristwatches. But nearly every president has encountered painful cases of this sort and has found them curiously influential in setting, subsequently, the internal atmosphere of his administration--not to mention the outsider's view of it.

Mr. Reagan evidently intends to pursue his own investigation. He owes it to Mr. Allen to arrive quickly at a decision whether to return him to his post at the White House. That's a gloomy task. But the president's first responsibility here is not to Mr. Allen. It is to his own office and the spirit in which he wishes to conduct it for the next three years.