Raising the issue at First Minister’s Questions on Thursday, the party’s justice spokesperson Jamie Greene pressed the Scottish Government and Nicola Sturgeon on whether any offender had escaped jail due to the presumption against short sentences.
Mr Greene said: "Figures released this week tell a horrendous story of domestic abuse in Scotland, which has risen for the fourth year in a row, with some 63,000 incidents last year.
"Second to our drug crisis in Scotland, this too is our national shame.
"Education and prevention of course are important but, First Minister, so is punishment. Let me ask how many perpetrators who would have historically received a custodial sentence did not under the government’s presumption against short sentences.
"If the answer is more than one person, we really have to ask ourselves what message does that send to the tens of thousands of victims of abuse, mostly women, about whose side justice is really on.”
Responding, Ms Sturgeon said the new domestic abuse legislation brought in two years ago accounted for more than half of the rise in incidents.
That piece of legislation widened the definition of domestic abuse to cover psychological domestic abuse and coercive behaviour.
The First Minister said: “One case of domestic abuse is one too many. We should have a zero tolerance approach and that is the approach the Scottish Government brings.
"It is because we have legislated to make more domestic abuse behaviour a criminal offence that we are seeing those numbers go up.
"Underlying these statistics is a sign that as a country, as a Parliament, we have taken this even more seriously.
"In terms of punishments, as Jamie Greene knows … I do not decide what punishment somebody gets once they are convicted of an offence. Yes we set the statutory framework for that but in terms of short sentences, it is a presumption against short sentences.
"The decision about whether or not any perpetrator goes to jail is not a decision for me or any member of the government. It is a decision for the judge presiding over that case and that is the way it should always be.”