The figures, which cover the years 2012-15, were released by the Scottish Police Federation (SPF),which said they highlighted the “idiocy” of not allowing officers to exercise their discretion in such cases.
Details obtained under freedom of information laws show that between 2012-13 and 2014-15 more than 58,000 people were remanded in custody in connection with domestic abuse.
But of those around 1,300 were released with no further action taken.
Calum Steele, general secretary of the SPF, said the figures “laid bare” the difficulties of a policy which did not allow individual officers to use their own judgment.
It followed Mr Steele’s comment to the Scottish Parliament’s justice committee on Tuesday that couples could no longer have a row without one of them “leaving in handcuffs” if police are called.
He told MSPs Scotland’s courts are being overburdened with domestic abuse cases which have no realistic prospect of a conviction due to insufficient evidence.
Marsha Scott, chief executive of Scottish Women’s Aid. said: “It really clear to us from the number cases where there’s a police call – 60,000 in this past year – against the number of cases the police report to the Crown for prosecution that there’s lots of judgments call being made.
“It’s a big mistake to assume that because someone was lifted and not prosecuted that there wasn’t a very good argument in terms of safety for lifting that guy for a short period of time.
“Can you imagine if we were having this discussion about sexual assault cases – would anyone suggest we not prosecute them because we have a low conviction rate? No.
“While policing in Scotland is probably the best in the world on domestic abuse, it is still far from good enough.”
Police Scotland said its officers are able to use their own professional judgment.
Chief Superintendent Barry McEwan said: “Officers across Scotland attend reports of domestic abuse incidents on a daily basis.
“When attending these incidents, our officers apply their professional judgment. Should officers determine a crime has been committed and there is sufficient evidence that the perpetrator is responsible, officers will, in line with Scots law, detain or arrest them.”