I know every branch is different, but Air Force cops have jurisdiction to chase a suspect from base into the city. So I’m sure they did do a chase. It was obviously dark at that time. But I mean come on. It was already known he should’ve been a high suspect due to the allegations, and suspicious activity of her getting called in. I guess my thinking is different. I just would assume they would have people watching his every move. In the Andreen McDonald case, they were parked outside his house everyday until her body was found.
I know it’s different. I just would’ve imagined they would’ve been tailing him. Just a thought.
Also, many of the Army (in particular) posts have civilian agencies that do the base security for check-ins, which may have really limited their resources for giving chase. I can't imagine, ever, that Army MPs would hop in their cars and chase him off post, much less someone like "Pond Security".
When I was stationed stateside, I could totally see someone running off post and not being pursued by the MPs. In that case, the local authorities would be alerted, etc. I honestly just cannot picture MP vehicles giving chase to a runaway car or person on the busy highway immediately outside Fort Campbell (in particular). Talk about civilian protests, lawsuits, political drama aftermath, etc.
Speaking of, I think that a major factor for particular parts of this case is the current political climate. (Nothing to do with race, please don't take it that way) There has been a major uproar against things like facial recognition, apprehension procedures, etc. When I was stationed in the Germany, my children attending DoD schools in 2018. The schools were VERY PC...meaning that children could cuss out teachers and do other very bad things, but merely speak to the principle about their feelings. However, if offensive words (even things as trivial as "stupid" or "dumb" were used) then there was harsh repercussions for being offensive. Anyways, all of this bundled together leads me to belief that any military suspect (regardless of race, gender, etc) must be handled with extreme caution, and the "innocent until guilty" mantra must be highly exhibited.
TL;DR version: I don't think the current MP/security forces for the base have a lot of control or reach off-post and must take a lot of caution now for potential suspects.