IS THERE A Republican or a Democratic way for a state to distribute license plates? Well, in the state of Indiana there is. Indiana, divided from its neighboring states of Ohio, Michigan, and (for most of its boundary) Illinois by nothing more substantial than a dotted line on the map, nonetheless continues to nourish a political culture that its 19th-century politicians -- you remember President Benjamin Harrison and Vice President Thomas A. Hendricks -- would recognize. Not every state and local government job is allocated by political bosses any more, but many still are; and until very recently Indiana voters were nonplussed when it was mentioned that government employees had to "contribute" 1 or 2 percent of their salaries to their elected official's political party. Who else should get it -- the opposition?

But now Indiana's dominant Republican political machine is preparing to get rid of one of the last vestiges of Indiana's patronage politics. This is the system of distributing license plates. The secretary of state has 183 license plate branches in the state's 92 counties, each of which is run by his appointee as a profit-making enterprise. In rural counties, this is small potatoes; in metropolitan counties, profits are said to range up to $200,000. But no lunch is free. The branch operators are expected to and do contribute money to the secretary of state's party -- right now, the Republicans. In 1984 that amounted to some $400,000. Also, another $400,000 or so from revenues for personalized license plates are split between Republicans and Democrats. So whenever an Indiana car owner renews his license plates, he's contributing either to the Republicans or to both parties.

In some states, eager-beaver lawyers are bringing lawsuits against such arrangements, arguing that they infringe somebody's freedom of speech. It's not likely that Indiana judges, appointed as they are by a thoroughly partisan process, would agree -- unless, maybe, it would hurt the other party. But as it turns out, it is the political process that is ending this political arrangement. The Democratic candidate for governor last year, Wayne Townsend, argued for bringing the branches under state control, in tones that may have suggested to naive non-Hoosiers that he had suddenly, after all his years in the Indiana Senate, discovered that politics was playing a part in government.

Mr. Townsend lost, but Gov. Robert Orr has now proposed a law for state takeover in 1988, and it's expected to pass in the Republican legislature. The Democrats hoot that this gives the Republicans another couple of years' contributions. But what is important is that the system is likely to end. Mr. Orr, a hard-headed politician who presides over an efficient political machine, has evidently decided that even in Indiana the contributions that political patronage can produce aren't worth the votes they might cost.