On the flip side, if there is something on it, releasing it could spook a perp or perps into killing Jayme out of fear of capture. It could even lead to a wrongful arrest: someone calls in and says they know that voice. Police check it out, the voice seems to match. The person lacks a credible alibi, and seems nervous (because who wouldn't be nervous if they were innocent and being looked at for this crime!?). Police spend time following this information which ends up not being the right person for the crime, or worse, the person ends up wrongfully convicted, police close the case, and the real perp walks... Hey, it could totally happen, though I'd like to think its unlikely to.
Ideally, they release the tape IF there is something that could HELP locate Jayme safely, but if the tape can't help, or could lead to greater danger for her, then hell no.