At this point, it's clear that Carl Crawford has moved on from his April slump. Well, as long as you aren't looking at his overall season line, it's clear: the Red Sox high-priced free agent is at just .235/.269/.362 for the year despite his productive May, underscoring just how terrible he was in April.
Luckily for Crawford, the season is more than two months long, and he still has June through September to finish righting this ship. His .304/.328/.482 line in May was a good start; while the on-base percentage is lower than you would like (and gives weight to the idea that he is not an ideal leadoff hitter, despite his extensive skills on the bases) he has shown power and ability to put the ball in play to make up for it, and even won AL Player of the Week honors for last week's performance.
There are still some concerns over his production, but luckily none of those are considered to be long-term issues. For one, Crawford hasn't yet hit well at Fenway--he has just a 532 OPS at home partially thanks to having exactly zero homers there. Fenway is a decent fit for Crawford because of his swing, though, and it's a rare player--left-handed or otherwise--who ends up hitting .220 at hitter-friendly Fenway over a full season, especially when that player is as good as Crawford.
Second, he has been abysmal against left-handed pitching. Crawford has never been good against lefties--his career sOPS+ (that's OPS for a particular split relative to the league's performance in that split) against southpaws is 77 (where 100 is average). This year, his sOPS+ against lefties is 2--yes, 98 percent below average, thanks to hitting .106/.157/.167 against them.
In his career, Crawford has hit .263/.309/.373 against southpaws. Again, not great by any means, but certainly tolerable, especially when you consider the extra runs he helps produce on the bases or the runs he saves with his stellar glove in the outfield. His career BABIP against lefties, in 1662 plate appearances, is .312 (compared to .335 against righties)--he just doesn't hit for much power against them, and tends to strike out more often than against righties.
This year, Crawford has a BABIP of of .120 against lefties, over 70 plate appearances. That's terrible, but the more important figure is the 70 plate appearances; it's just not very many at all. Just as Crawford's production rebounded from April to May, you can expect his BABIP against lefties to shoot up closer to his career rates. With the hole he has dug himself already, chances are good this will be a poorer season than usual against left-handers---adding just one hit in 29 May at-bats against lefties didn't help any--but betting on him to finish this far below his career norms over the course of a 162 game season wouldn't be the best gamble you've ever made.