'House Democrats know they have no legal right to these documents, but their shameful and cynical politics know no bounds, ' Grisham said in a statement.
President Donald Trump last week abandoned his bid to inject a citizenship question into the census, after the Supreme Court said the administration's justification for the question "seems to have been contrived".
The Justice and Commerce departments have produced more than 31,000 pages of documents to the House regarding the census issue, and senior officials from both agencies, including Ross, have spoken on the record about the matter, the White House said, adding that Democrats continue to demand documents that the White House contends are subject to executive privilege.
Trump's announcement was preceded by a Supreme Court decision that blocked the citizenship question from being added.
That setback pushed President Trump off of adding the question to the census, leading him to instead opt for an executive order to compile the citizenship data from existing federal databases.
The top Republican on the committee, Jim Jordan of OH, countered that both agencies under Barr and Ross have submitted more than 31,000 documents to the committee and made "all kinds of witnesses" available for questioning, including Ross himself.
They maintained the vote is "degrading the constitutional separation of powers and [the House's] own institutional integrity".
Democrats have also held former White House counsel Don McGahn in contempt, and are eyeing a citation for presidential counselor Kellyanne Conway as well.
The 230-to-198 vote comes after both Barr and Ross failed to comply with subpoenas calling for documents to related the Trump administration's attempt to add a citizenship question to the 2020 census.
A spokeswoman for Barr said the contempt vote defied logic and undermined Congress' credibility with the American people. The Committee has short-circuited that production by pursuing this premature contempt resolution, choosing instead to focus on a small subset of privileged documents.
The House voted Wednesday to hold Atty.
Despite the battle over the census being settled, Mr. Cummings said the contempt citation and their investigation was still necessary.
The secretary dismissed the vote as "just more political theater", and noted that his department had handed over thousands of pages of documents over to the committee already.
Democrats on the House Oversight Committee say they need these documents as part of their probe into the origins of the citizenship question among Trump administration officials.
The move marks the second time a sitting attorney general has been found in criminal contempt by the House.
Wednesday's vote goes further than previous contempt motions in this Congress so far because it's elevated to the level of criminal contempt, which would typically refer the matter to the Justice Department.
However, the motion is mostly symbolic as the DOJ - essentially Mr. Barr - is unlikely to take any action against himself or Mr. Ross.
"We may be in July, but it's Groundhog Day all over again", House Minority Leader Kevin McCarthy (R-Calif.) said. Brindisi, D-Utica, stood out as one of only four Democrats to vote with a unanimous caucus of 194 Republicans against holding Barr and Ross in contempt.
The United States and China still have to work through major issues to reach any trade agreement, including intellectual property theft, structural reforms and subsidies, U.S. Commerce Secretary Wilbur Ross said on Thursday.