There is a runner on third with one out and batter hits a ground ball to first baseman who opts to throw home before stepping on bag or tagging batter. The runner is safe at home and the batter is safe at first. Is the batter awarded a base hit and a RBI?
In general, it would be credited as a hit and an RBI.
The only question is that you didn't say why the runner was safe. If the runner beat the throw, then it's a hit. If the first baseman threw wildly or the catcher dropped the throw, then you could credit an error instead of hit/RBI.
The decision to throw home though would never be counted as an error, even if it had no chance of succeeding.
It certainly would be in baseball, it would be an infield single, and the hitter would be credited with an RBI and a base hit. Typically softball leagues try to stick to MLB rules when they have no official definition for the issue at hand, so unless if for some reason the people in charge of the softball games had some particular reason to do things differently then it would be.
Admittedly I'm more familiar with baseball than softball, but for a situation like this, I think the statistical rules are the same. That said, there are a couple of possibilities for the scoring here, and that is with the assumption that no error has been charged to a fielder; i.e. that the throw home was accurate, but the runner from 3rd simply touched home before the tag was applied:
- Hit and RBI: In the opinion of the scorer, the batter would have reached first with normal effort by the defense if the defense had attempted to make the out at first instead of attempting to get the out at home.
- Fielder's choice and RBI: In the opinion of the scorer, the batter would have been out at first with normal effort by the defense if they had attempted that play.
If the assumption that no error is made is incorrect, that introduces more possibilities that I won't enumerate here, although a hit will probably not be awarded and an RBI is doubtful also.