Yes, they did. It was confirmed today by Justice Department spokesperson Kerri Kupec. Here is what this CNN article says:
The Office of Legal Counsel later said the complaint could be looked at as a possible criminal matter, sending it along to the department's Criminal Division, according to a legal memo released Wednesday. Around the same time, Atkinson, who had first heard from the whistleblower, also referred the matter to the Justice Department.
Together, those notifications kicked off the Justice Department's probe of whether there was a possible violation of a campaign finance criminal statute. Justice's Criminal Division took the lead. Prosecutors obtained the summary transcript of the call from the White House, and prosecutors confirmed with knowledgeable people at the White House that the five-page document was the best evidence available, according to the officials. They did not interview any to gather more facts....
The follow day, September 4, inspector general Atkinson spoke up again, this time to the FBI. With the Criminal Division at work, the FBI deferred to the prosecutors. Two more weeks went by, with career public integrity prosecutors looking at the matter, according to the officials. Then sometime last week, the Justice Department made its final determination: no reason for a full-blown criminal investigation. What the President asked of Ukrainian President Volodymyr Zelensky couldn't amount to a quantifiable "thing of value" under campaign finance law, top administration officials determined. Criminal Division assistant attorney general Brian Benczkowski made the final call, the senior DOJ officials said. The Office of Deputy Attorney General Jeffrey Rosen was also involved with the legal analysis, as were the heads of the National Security Division and the Office of Legal Counsel, the officials said.
"All relevant components of the Department agreed with this legal conclusion," Justice Department spokesperson Kerri Kupec said. Attorney General William Barr, for his part, had "minimal involvement" in the Justice Department's handling of the referral, an official briefed on the matter said.