What does evaluation mean? Does that mean they get hauled off to a hospital against their will for a few days or does it just mean someone stops by to talk to them?
Barring an explicit threat, it would need to be a multi-stage process, with some additional caveats.
Initial process
1. Posting is flagged by software, or reported by other users for review
2. Reasonable human looks over it. (Bonus; this would require many social media companies to outsource to the real world, thus creating jobs outside California.)
3. Supervisor confirms human's assessment and forwards to LE.
Professional evaluation phase
4. LE agency assesses, and decides to move forward.
5. Someone with proper mental health and threat evaluation skills assesses the posting. Each step from here on needs to have a progressively higher "continue the process" bar.
Direct evaluation and action phase
6. Someone with proper mental health evaluation skills makes contact with the poster. This would be the first time the subject knows anything is being done.
7. Independent outpatient evaluation at the person's convenience.
8. Involuntary commitment for final evaluation and treatment.
The step 5, 6 and 7 evaluations should be in two stages; first a "clean slate" assessment of only the current situation, then once that is complete and fully documented, the evaluator should be given access to all relevant history for an overall assessment. (Obviously, in some areas, this won't be possible on repeat investigations, since there may only be a few people in a reasonable distance with the proper training. However, by that point, the process should be moving either towards action against the subject or a full investigation of possible harassment.)
At any step, the evaluator should be able to stop the process entirely, at which point all steps leading up to that should be subject to internal and then independent review to determine whether it was reasonable to even start the process, and those improperly advancing it through the process should be held liable if it's found unreasonable. (Since we all know there are liberal CLEOs out there who would use this to harass various gun owners and others, and step 4 is the first point at which liability should be significant - it's not reasonable to expect every forum to have a staff of professional threat assessors, but any LE agency should at least have access to someone trained in that.) They should also be able to put the process on hold if it's somewhere between "this is nothing" and "this requires further action at this time." In any case, all records would be kept at both local and state level unless a completely unfounded complaint is ordered by a court to be removed or sealed. Obviously, if there's sufficient evidence of truly illegal activity, then the normal criminal process can take over at any point as well.
Barring a definite illegal act that would allow the court to order confinement anyway, though, step 8 should require two or more completely independent evaluations that unanimously conclude the person is a clear threat to others and a court order to make it happen. Most likely, at least stage 8, and possibly 5, 6 and 7 as well, would be handled at the state level. 4 should probably be handled locally, but with direct state oversight. (i.e. state should be getting copies of everything for step 4 and beyond, whether they handle it prior to 8 or not. This way, local LE have the chance to say "yup, Earl's been a problem for years, but we've never had the ability to move forward with anything yet" or "Earl runs his mouth a lot, but he's got severe Parkinson's and no legs, so he's not really going to do anything," while the state will be able to see that they have 7,960 credible reports against the mayor's son but have immediately dismissed each one as unfounded so as not to risk his probation from when he got busted out of state where they couldn't protect him.)
Of course, all costs need to be borne by the state and/or local government. The subject should not be held liable for any cost of an evaluation demanded by the state, and plenty of people simply can't come up with a few hundred extra to go pay a counselor or psychologist for the office visit. This would also discourage abuse of the system at the LE level, since they're going to have to justify the cost of any evaluations ultimately deemed unnecessary to the same people who determine their budget.