The result comes as the survey also confirms a trend in the polls, with No leading for the first time in this series of polling.
The poll, conducted for The Scotsman by Savanta ComRes, interviewed 1,009 Scottish adults aged 16 and over between March 5 and 10.
The survey is one of the first major polls with fieldwork after both Nicola Sturgeon and Alex Salmond gave their evidence to the ongoing Holyrood inquiry into the botched handling of harassment complaints.
It also shows favourability ratings for the First Minister and the Scottish Government continuing to plummet from pre-Christmas highs as Prime Minister Boris Johnson and the UK Government see improvement in their popularity.
The poll is the first of this series of surveys to show the SNP on the edge of a majority rather than comfortably achieving one.
Asked who they would vote for in their constituency vote, 48 per cent of Scots said they would vote for the SNP, down 6 per cent from the equivalent poll in February.
The SNP’s vote is also down in the regional list, with 40 per cent of Scots saying they would vote for the party, down 3 per cent compared with last month.
These numbers are in line with the result from 2016 where the SNP received 46.5 and 41.7 per cent of the vote, leading to the return of 63 seats in Holyrood.
It is also another strong showing for the Scottish Conservatives, with 23 per cent of Scots backing them in the constituency ballot, the same as February, and 24 per cent backing Douglas Ross’ party in the list vote, up 4 per cent.
Scottish Labour have been the main beneficiaries from the SNP’s drop in support in the constituency vote, with 20 per cent of Scots saying they would vote for new leader Anas Sarwar’s party, their joint strongest performance in 2021 and up 4 per cent from February.
However, the party has made no gains in the list in returning 18 per cent of the vote, according to this poll.
The Scottish Liberal Democrats could also be set for an improvement in the constituency vote with 8 per cent of Scots, up 3 per cent, with their performance on the list unchanged from February on 6 per cent.
The Scottish Greens have also seen their vote share on the regional list stay the same at 10 per cent.
Such a result in May would see the SNP miss out on a majority by one seat, returning 64 MSPs, one more than in 2016.
It would also see the number of Conservative MSPs drop from 31 to 30, and Labour’s representation drop from 24 to 20, with the Liberal Democrats retaining their five MSPs.
The Scottish Greens would be the party who gain the most, with an increase of four seats up to ten, which would be their best performance in any Holyrood election to date.
These numbers are very similar to those in the Sunday Times/Panelbase poll from Sunday, in which polling expert Sir John Curtice predicted a slender SNP majority.
The poll is also the second to show a lead for No should a Scottish independence referendum be held tomorrow.
A total of 45 per cent of Scots would vote Yes if the vote was held tomorrow, with 47 per cent saying they would vote No and 8 per cent saying they did not know.
With don’t knows removed, this leads to No leading with 51 per cent of the vote against 49 per cent for Yes, confirming the general downward trend for Yes over the past few months.
These figures are directly comparable to Savanta ComRes’s February poll for The Scotsman, which showed a Yes lead of 53 per cent and No returning 47 per cent.
The result comes after the first poll in this series, recorded in December, had shown support for independence at an equal record high. With don’t knows excluded, the December poll showed 58 per cent of voters intending to vote Yes, with 42 per cent voting No.
It comes as trust in Ms Sturgeon continues to decline amid her public battle with Mr Salmond and the continued success of the vaccine rollout.
The First Minister’s personal approval ratings are down by 11 per cent, with a net favourability of 17 per cent, when compared to the first poll in this series in December and down nine points since February.
Favourability towards the Scottish Government has also taken a steep dive, down 13 per cent when compared to February, with a net favourability of 11 per cent. This is down 6 per cent when compared to December.
Mr Johnson meanwhile has seen a similar level of improvement in his approval ratings, rising by 14 per cent when compared to December and up five points since February, now sitting at a net favourability of -30 per cent, still well below Ms Sturgeon.
Opinion of the UK Government has also improved, rising 14 per cent to a net favourability of -20 since December and up six points since February.
Commenting, associate director of Savanta ComRes Chris Hopkins said: “While the headline here may look bad for the SNP, and the natural conclusion to draw that the Salmond inquiry is having an impact, but ultimately the facts remain that, on these Holyrood numbers, the SNP would likely be incredibly close to forming a majority under an electoral system not designed for majorities.
"While the inquiry continues to play out, it’s still worth remembering how far away both the Conservatives and Labour are from really denting the SNP’s dominance and it would take a complete capitulation to change the likely outcome at the Holyrood election in May.”