The case is Pittman v. Garcia. You can read the Complaint (including the challenged social media policy as an exhibit) here.
The Houston Press has a concise summary of the policy, including some extraordinarily broad provisions:
Under the new policy, HCSO employees risk disciplinary action if their Facebook or Twitter posts "cause undue embarrassment or damage the reputation of and/or erode the public's confidence" in the sheriff's office. Posts containing any HCSO logos, badges, or personal photographs that show employees in HCSO garb or uniform are prohibited without prior approval from a chief. Also: "speech containing crude, blasphemy (sic), negative, or untrue claims about the HCSO and/or any HCSO personnel is forbidden and therefore will be grounds for disciplinary action." Similarly, HCSO employees now face disciplinary action for any comments on social media that "negatively affect the public perception of the HCSO."HT to my Mason Law classmate, Josh Blackman, for the links.
Public employees enjoy some First Amendment free speech protections. Generally, they maintain the right to speak as citizens on matters of public concern, which must be balanced against the public employer's right to operate efficiently and effectively. The Supreme Court created a notable exception in Garcetti v. Ceballos in that employees speaking in their official capacities are generally not protected.