The party’s health spokesman Anas Sarwar has written to Holyrood’s Health Committee asking members to to take evidence from NHS boards across the country to help reassure the public over charity cash use.
He has also written to the Audit Committee asking it to re-investigate the financing and accounts at NHS Tayside.
Mr Sarwar has backed his party colleague Jenna Marra’s call that senior managers who have left the health board after the scandal should not get “golden goodbye” payoffs.
NHS Tayside chairman Professor John Connell stood down on Friday after Health Secretary Shona Robison called for him to quit when it emerged NHS Tayside had apparently used donations to fund new technology.
He has been replaced by NHS Greater Glasgow and Clyde chairman John Brown on an interim basis.
Earlier this week it emerged NHS Tayside took more than £2 million from its endowment fund - which is made up of donations from the public or bequests in wills - to cover general running costs, which could normally be funded from its core budget.
It was reported to have used the endowment fund when “faced with a funding deficit” in 2013-14, and that its constitution was temporarily suspended to enable this, as the money was going to retrospectively fund projects already approved by the board.
The health board was bailed out with a Scottish Government loan of £33.2 million in 2016-17.
Mr Sarwar said: “The scandal at NHS Tayside has seriously damaged public confidence in our NHS.
“That is why it is essential all NHS boards are now called before the Health Committee to establish how this came to happen and if it is more widespread - starting with NHS Tayside.
“The public need and deserve urgent clarification from other health boards on whether any funds have been misspent elsewhere.
“The Audit Committee must also urgently re-investigate the SNP’s financial mismanagement of NHS Tayside, which caused this scandal in the first place.
“SNP Health Secretary Shona Robison appointed John Connell to sort out NHS Tayside after years of chronic mismanagement by the SNP. It would be an outrage if senior managers now received any kind of golden goodbye.”
He repeated calls for the Health Secretary to “consider her own position”.