Has an Olympic Hockey (Women) game ever ended 3-3?
Exactly once. On February 8, 2001, Japan and Germany drew 3-3, and no Olympic Hockey (Women) game before or since has ended that way. When it happened it was a scorigami, the first 3-3 in league history.
That makes 3-3 the 27th most common final score out of 41 that have ever occurred in Olympic Hockey (Women). One point away, 4-3 has happened 3 times and 3-4 has happened never.