I work primarily slow-pitch rec ball (with some of the big boys thrown in once or twice a week), and usually will ask the coaches at the pregame meeting if they have anyone keeping score and point out the person to me. I don't check with that person unless I think the run rule will come into effect.

As for umpires turning in scores, one league I work doesn't do that while the other does. The league that doesn't require the umpires to turn in scores asks the teams to do that via a scoreline page on their website or by phoning in the morning after. I understand if there's no score reported within 48 hours, it goes down on standings as a double forfeit until someone turns in a score. Gives the accountability onto the teams to make sure their records are right, etc.

The other league provides tons of scorecards, and drop boxes at both entrances to the complex to drop them off so the maintenance guys will collect them the next day and drop them off at the city rec offices. Nice system. But ultimately, the teams are still responsible for making sure everything's right in the standings on the rec department's webpage.