Liam McArthur MSP, the party’s justice spokesman, has asked for assurances on the matter in a letter to the justice secretary Michael Matheson.
The letter comes after new figures showed that since 2013, 64 people have died while in prison yet the reasons remain unknown.
Analysis of a Parliamentary Question lodged by Mr McArthur shows that since 2013, there have been 64 ongoing fatal accident inquiries (FAI), with an increasing backlog of unresolved FAIs.
This analysis came after it was revealed half of the deaths in Scottish prisons in the last five years remain “unexplained” because of a failure to reach a conclusion in fatal accident inquiries.
Mr McArthur said: “These figures show that a growing number of prisoners’ deaths have yet to be properly investigated.
“Each year a case goes unanswered is another year that family and friends of the deceased are left in limbo.
“The Scottish Government must explain why this backlog has been allowed to develop and what steps it is taking to reduce it.
“For families not to have the answers as to what happened to their loved one is a real injustice.
“I urge the Scottish Government to bring forward the necessary legislation that will make sure that all future fatal incidents are properly investigated.”
A spokeswoman for the Scottish Government said: “Our thoughts are with the family and friends of the deceased for whom it must be a difficult time.
“Any death in custody, including prison, is properly investigated through an FAI which is a matter for the Lord Advocate.”
A Crown Office spokesman said: “The Crown Office and Procurator Fiscal Service (COPFS) aims to hold Fatal Accident Inquiries as soon as practicable.
“Most death investigations conclude once a cause of death is known and, in the case of a death in custody, a FAI will then be held.
“Some cases require further investigation before the Crown can proceed with a FAI. The investigations may involve complex technical and medical issues requiring the instruction of experts.”
COPFS said there are also factors not under its control which can contribute to delays, while a number of 2013/14 deaths currently recorded as “not determined, awaiting FAI” have concluded and await the Sheriff’s determination.
Others are near completion or awaiting dates for a FAI to be set.