Sues the police? They're unlikely to have had Woods in lockup for more than a few days at most, and qualified immunity will most definitely apply.
It's either the county or state that had Woods incarcerated, and that will likely have been at the order of the court. The state is what you go after for false imprisonment, not "the police". (In theory the police can be sued for false arrest, but in this case there was evidence — bogus, but evidence nonetheless — supporting a possible crime.)
Frankly, I don't think Woods would have a case against the state, either. It's a shame, but Keirans did a pretty good job of flipping the frame around. It's not like there was gross prosecutorial misconduct here. Had Woods been able to afford an independent investigation he might well have been able to escape a miscarriage of justice, but he was indigent. The article doesn't say whether there was a trial (probably a bench trial) or if Woods took a deal or what, but I don't like his chances whatever choice he made.
I'm as opposed to police and prosecutorial misconduct as anyone I know, and this case is certainly shameful, but I can't honestly say I see a gross violation of ethics by the California authorities in this case.
Note the truth only came out after the hospital — Keirans' employer — paid for what was presumably quite an expensive private investigation. (And kudos to them for that.) The detective presumably had to do some groundwork to get that DNA sample from Woods' father for comparison; it's not like he just read the file.
District courts in the US have to churn through a huge caseload. This one would have looked a little odd, but not enough to raise any alarm bells. Someone said "maybe this guy has mental issues" and moved him from jail to a treatment facility, which in the US counts as a beneficial outcome. Woods was hard done by, but someone tried to make it a little easier on him.