In Batman’s case, Commissioner Gordon is certainly a person for whom the State is responsible, and Batman often acts together with Gordon and obtains significant aid from Gordon in the form of information and evidence. Batman’s conduct is also otherwise chargeable to the State because the Gotham Police Department has worked with Batman on numerous occasions (and thus knows his methods) and operates the Bat Signal, expressly invoking Batman’s assistance in a traditionally public function. This suggests state action under the public function theory: “when private individuals or groups are endowed by the State with powers or functions governmental in nature, they become agencies or instrumentalities of the State and subject to its constitutional limitations.” Evans v. Newton, 382 U.S. 296, 299 (1966).
In the real world, this would cause significant problems for Batman and Gotham. Batman’s rough and tumble style would lead to a rash of Section 1983 claims for damages and probably also for an injunction against Batman’s future cooperation in police investigations. As discussed earlier, most evidence that Batman collects would be inadmissible, and police use of that evidence might bar the use of additional evidence collected during a subsequent police investigation.
Now, clearly none of this is the case, so there are three possibilities. Either all of the criminals in Gotham have incompetent attorneys, the state action doctrine in the DC universe is weaker than it is in the real world, or Gordon has actually managed to keep his reliance on Batman a secret. I’m going to opt for the second explanation. Superheroes like Batman are simply too effective for a court to shackle them with the Constitutional limitations of the state, especially with supervillains running around. Perhaps the DC universe courts have developed a public emergency or necessity exception to the state action doctrine whereby private individuals pressed into public service in an emergency are not held to the same standards as ordinary state actors.