Two more arrests have been made in the UK this week as part of a joint police and FBI investigation into the hacktivist activities of the group and its offshoot, LulzSec.
In an online posting, Anonymous said the attack was in retaliation for the arrests of dozens of alleged members of the group, including Jake Davis, arrested in the Shetland Islands in July, and 14 people arrested in the US in connection with denial-of-service attacks on Paypal in December 2010.
The attack on Paypal was linked to denial of service attacks on Visa and Mastercard for blocking donations to the whistle-blowing organisation WikiLeaks led by Julian Assange.
"For every defendant in the Anonymous 'conspiracy' we are attacking two top Texas police chiefs, leaking 3Gbytes of their private e-mails and attachments," the posting said.
The posting ends with a list of names, e-mail addresses and controversial topics, actions and statements detailed in private e-mails sent by the named police officers.
In a Twitter posting, Anonymous claimed that it had brought down the police website for more than three hours.
In another Twitter posting, the hacking group claimed it had taken down the website of the United States Courts for the Ninth Circuit. "You argue civil disobedience is cyber-terrorism. We think not," the posting said.
This story was first published by Computer Weekly