The sale of Conrail, the government's railroad, is proceeding conspicuously slowly. It is turning into a marvelously clear and detailed illustration of all the difficulties in transferring a large federal operation to the private sector. President Reagan, in his budget message last February, made much of his intention to get the government out of the businesses in which it competes with private industry. Unlike most of Mr. Reagan's other examples, Conrail ought to be under private ownership. But the chances of a stalemate are rising.

The Senate, early in February, passed the administration's bill to sell Conrail to another railroad, the Norfolk Southern. Conrail has an uncertain economic base, the administration argues, and needs an alliance with another road to guarantee its survival in good health. The House remains skeptical. Selling Conrail to Norfolk Southern would join the major railroads of, respectively, the Northeast and the Southeast. That raises obvious antitrust issues, and the House Energy and Commerce Committee is unlikely to take any action until the Justice Department completes its study of the implications for competition. That won't be until June. At that point Congress would have to be prepared to act rapidly or, in this short election-year session, it will be unable to act at all.

The questions are not only to whom to sell Conrail, and under what conditions, but for how much. The price in the Senate's bill is the $1.2 billion that the administration negotiated with Norfolk Southern, but the other bidders have now gone higher. The railroad's future financial health, rather than the selling price, ought to be the chief consideration. But the House is unlikely to vote to sell at the low bid. Alternatively, the House might vote simply to auction off the stock in a gigantic public offering. But that, the administration fears, would create a stalemate between House and Senate, deferring any hope of passage until another year and another Congress.

And then there are jobs. Because it initially feared that Conrail might actually collapse, Congress gave Conrail's management extraordinary latitude to cut unprofitable routes and lay off unnecessary labor. That won't last forever. If the railroad remains under federal control, you can take it for granted that presently Congress will succumb to the temptation to begin doing little favors for its friends in the matter of routes and job protection. That's an important reason for acting now.

There are several acceptable ways to sell it. Joining it to Norfolk Southern is probably still the best. But any of the several would be preferable to endless indecision and paralysis. Unfortunately, indecision and paralysis are becoming increasingly likely.