I volunteer in Texas and we do not have any requirements that involve more "in-depth" training (PD, EMT, Fire, etc.) past ICS 700, 800, and that kind of simple stuff (We do require EMT-B in order to be credentialed with our MD, but that's a different story). That said, we adjust who we on-board depending on our needs at the time, which may involve preferring folks with experience and certifications. But no, no Reserve LEO requirement here. That said, I do not know of any teams in Texas that are identified as volunteer SAR that have this requirement.
Regarding helpful qualifications, it really depends on what type of team it is. For instance, the team I am on does technical rescue in addition to ground and canine SAR, but one of our sister teams is strictly canine search. That said, pertinent qualifications help. For us, certifications within civil services helps big time. As well, having taken SAR and ICS related courses is a bonus. Same stuff that would build your resume.