Warning: The following contains SPOILERS for Batwoman season 3, episode 12, "We're All Mad Here."
Jason Todd's death at the hands of Joker in the post-Crisis Arrowverse was confirmed in Batwoman, though it remains to be seen if he was resurrected and became the Red Hood in this reality. The reference to the rebellious Robin's death also raised the question of just what happened to the rest of Batman's followers in the Arrowverse. While Batman's history in the Arrowverse has been extensively chronicled, almost nothing has been said about his young partners, beyond a single confirmation Robin existed in one Vesper Fairchild broadcast.
The action of Batwoman season 3, episode 12, "We're All Mad Here," centered around the search for one of the Joker's special joy buzzers, which had the power to make someone as crazy as Joker or restore sanity to a lunatic through a precisely calibrated shock. The anti-hero Alice, who sought the joy buzzer as a cure for her own increasing mental instability, was the first to find it in the hands of former Arkham Asylum inmate Kiki Roulette, who had once been employed by Joker as his personal toymaker. Alice browbeat the mad inventor, but Kiki laughed off her threats, saying that it was a good gag, "...nothing beats the one about the time I helped the Joker beat Robin to death with a crowbar." The series silently eluded to this one episode earlier, when the Joker's old hideout was shown to have a bloody crowbar in a glass case. In both instances, the bloody crowbar was a reference to the death of Jason Todd, the second Robin, who was beaten with a crowbar by the Joker and left for dead in an exploding warehouse in the classic Batman storyline A Death in the Family in 1988.
With Jason Todd confirmed to have been Robin in the Arrowverse and having died a similar death as his comic book counterpart, the question is raised as to whether or not he might also have become the Red Hood. On the one hand, it seems unlikely, given that the Arrowverse Batman reportedly killed Joker. This would leave a resurrected Jason Todd with no reason to rebel against his mentor by adopting Joker's first criminal identity. Additionally, there have been no previous references to Jason Todd or the Red Hood.
However, there is also evidence to the contrary. Batwoman has gone out of its way to avoid establishing anything firm about most of Batman's family from the comics, so this lack of information is not unusual. It is equally unclear, for instance, if Barbara Gordon ever became Batgirl or Oracle or if Dick Grayson became Nightwing and moved on to Blüdhaven in the post-Crisis Gotham City. (It should be noted that Arrow previously teased the existence of Oracle and the tie-in book Oliver Queen’s Dossier confirmed Nightwing's existence in an e-mail to Amanda Waller, but that was before Crisis on Infinite Earths.)
Whether or not Jason Todd became the Red Hood in the post-Crisis Arrowverse, the establishment of his existence on Batwoman comes at an auspicious time. Recent reports confirmed that actor Jensen Ackles is tied to a DC Comics project, which is also being overseen by Arrowverse boss Greg Berlanti. Ackles previously played Jason Todd in an animated adaptation of Under The Hood and has voiced an affinity for the character, having dressed as him for Halloween in 2018. While this does nothing to directly confirm that Ackles' project might be a Red Hood series set in the Arrowverse, the possibility is sure to excite those fans who have long hoped to see Ackles play Jason Todd in a live-action production.