Prosecutors are considering whether to charge Mairtin O Muilleoir for retweeting the controversial Barry McElduff Kingsmill video.
The Public Prosecution Service has received a file from the PSNI after detectives interviewed the South Belfast MLA on Thursday.
Mr O Muilleoir confirmed yesterday that he had been interviewed by police.
He attended Musgrave police station in the city voluntarily, and was questioned by detectives in relation to three suspected offences; one under the communications act 2003, and two under the public order act.
Detective Chief Superintendent Tim Mairs confirmed that a man attended Musgrave police station voluntarily by prior arrangement.
Mr O Muilleoir said last night that he had been invited to attend what he termed a "short interview with the PSNI on a voluntary basis" and added that he was "happy to do so".
"I reiterated to the PSNI that I considered Barry McElduff's tweet to be entirely innocent and apolitical and retweeted on that basis," the former Stormont finance minister said.
The former West Tyrone MP posted a bizarre video posing with a loaf of Kingsmill bread on his head on January 5, the anniversary of the murder of 10 Protestant workmen near the village of Kingsmill. He insisted the video was not aimed at the victims, but later deleted it, publicly apologised and resigned as MP.
Mr McElduff was questioned by police in March following complaints about the video and a file was sent to the PPS.
A spokesperson for the prosecution service said last night that the issue was under "active consideration".
Victims' campaigners and a DUP MLA have welcomed the development in the police investigation.
Alan Lewis, from the Family Research and Policy Unit (FRPU), commended the PSNI on their handling of the investigation into the tweet.
"We must commend the PSNI for their dedication and continued liaison with the families; we welcome the manner in which this complaint and investigation have been handled," he said.
"The original tweet and subsequent retweet cased great offence to victims right across Northern Ireland."
Mr Lewis welcomed the police questioning of Mr O Muilleoir, and called on the South Belfast MLA to resign, as Mr McElduff has done.
South Armagh victims' campaigner Barrie Halliday also welcomed the development.
"I commend the police for the professional manner in which this investigation has been conducted," he said.
"I pay tribute to the families who have endured long years of suffering, a fresh inquest and these latest insults. Mairtin O'Muilleoir is one of Sinn Fein's so-called top strategists, and as such should be very aware that younger and less influential members follow his lead."
Newry and Armagh DUP MLA William Irwin said his thoughts yesterday were with the families of the Kingsmill massacre, and he paid tribute to them for their display of "great dignity and fortitude". He also called for Mr O Muilleoir to resign his Assembly seat.
"Michelle O'Neill should have sacked the former finance minister. At least Barry McElduff had the self-awareness to resign. Mairtin O'Muilleoir instead hid from the media, took a social media training course and clung to office," he said.
"Today, my thoughts continue to be with the families of the Kingsmill massacre as they once again display great dignity and fortitude."