The results of the Panelbase survey were published as Richard Leonard faces a rebellion from grassroots members after party chiefs said they could not debate anti-semitism at the conference in Dundee this weekend.
The poll of 1,002 Scots, which was commissioned by the Wings over Scotland blog and carried out from March 2-6, found that 19 per cent planned to vote Labour in their constituency at the next Holyrood elections - a drop of three per cent from June 2018.
When it comes to the list vote, Labour was also on 19 per cent - a drop of four per cent from last year.
The SNP remains unchanged on 41 per cent when it comes to constituency voting intentions, and 36 per cent on the list vote.
The Scottish Conservatives are unchanged on 27 per cent for the constituency vote and 26 per cent on the list.
The results are a further blow for the Labour leader in Scotland. Yesterday the party was rocked when senior MSP Kezia Dugdale said she had been “shocked” to learn that Mr Leonard had intervened in a pro-EU statement written by Labour MEPs Catherine Stihler and David Martin for the programme of the Scottish Labour conference, which opens tomorrow.
The Scotsman has asked Scottish Labour for comment.