Tl;Dr - Yes, for the sake of transparency and information sharing.
As protests become violent in some parts of the country, it's encouraging to see police departments use their social media accounts to show transparency and explain why police action is taken.
However, many agencies shy away from using social media during times of crisis because they may not want to devote resources to it, or due to fear of backlash.
Police should take into consideration that when they don't put their own message out others do it for them, and the narrative is shaped without their input. A one-sided narrative makes it harder to rebuild trust, and strains the already tense relationships. As for backlash, it will always exist, and the job of the police is not to get "likes" or 100% positive reinforcement, it's to inform the public and give information that might otherwise not be available. Some tips:
DO use twitter for warnings to crowds if you plan on taking police action. These tweets should mirror the warning given on the ground, not replace them.
DO show reasons for why a protest is declared a riot and why police action is needed.
DO stress that violence is caused by a small group (when it's the case) and that police action is not against protests as a whole.
DO encourage peaceful and respectful demonstrations, and show images of your officers protecting those.