'Problem play' is forceful but not quite convincing; Split Second Play by Dennis McIntyre. Directed by Samuel P. Barton.

''Split Second'' resembles what used to be called a problem play. The problem in Dennis McIntyre's troubling, explosive drama at Theatre Four concerns the dilemma that suddenly faces Val Johnson, a black detective, as he patrols a tough New York neighborhood on a dark Fourth of July evening.

Taunted with obscene invective and racial insults by a white suspect he has just handcuffed, Johnson goes momentarily out of control and fatally shoots the man.

From this riveting premise, Mr. McIntyre builds a psychological plot that in effect becomes a case history of Val Johnson (John Danelle). As Johnson wrestles with whether or not to falsify the facts in his testimony at a departmental hearing, ''Split Second'' conducts its own investigation into what triggered the detective's uncharacteristic behavior. Mr. McIntyre methodically - and with considerable repetition - develops his rationale for Johnson's ultimate decision. The outcome is understandable although the argument remains less than wholly convincing.

The performance staged by Samuel P. Barton seizes forcefully on all of Mr. McIntyre's salient points. In the difficult role of Val Johnson, Mr. Danelle comprehends the ambivalence and inner turmoil of a man of conscience and integrity struggling to reconcile two irreconcilable positions. Apart from a detached but discerning police superior (Helmar Augustus Cooper), Johnson's principal adversary is his father (Norman Matlock), an ex-cop who has lived both by the constabulary code and by the rigid rules of survival for a black man in racist America.

The lovely Michele Shay as Johnson's fiercely loyal wife and Peter Jay Fernandez as a fellow black detective serve the purposes of the play's dialectic and help influence Johnson's decision. Bill Cwikowski snarls derisively in the role of the hateful punk.