The woman was subsequently moved into a safe home with her children.
OT was aware of the relationship's violent history.
Oranga Tamariki regional manager Tasi Malu said the incident has been reported to their privacy team, who will be "assessing what other actions may be appropriate".
"We're working to assist the complainant and ensure they are safe and supported in the right way," he said.
The woman said she needed help with finding a long-term housing solution.
"I'm trying to make life work ... while I have a home that I'm paying rent on that I can't go to because I'm not safe," she said.
She said she had since accepted that Oranga Tamariki was genuinely remorseful in its apology and the two were in talks to remedy the error.
The Ministry of Justice declined to comment.
The search for emergency housing comes one week after Ministry of Social Development data revealed that there are now 3888 children living in emergency housing nationwide - 225 in Hawke's Bay alone.
As of December 2020, Napier led the way with the highest number of people on the Housing Register in Hawke's Bay (741), followed by Hastings (706), Wairoa (85) and Central Hawke's Bay (68).
Napier also topped the charts with the highest number of children on the emergency housing waiting list in the region 168), followed by Hastings (30), Wairoa (15) and Central Hawke's Bay (12).
According to the Ministry of Housing and Urban Development (HUD), Napier is top of all territorial authorities for public housing register numbers per capita.
A HUD spokeswoman said population growth in Napier - which was 9 per cent between 2013 and 2018 - has outpaced construction, while the Napier floods in 2020 also impacted available space.
MSD acting regional commissioner for social development Karen Bartlett earlier said there was a shortage of affordable housing in Hawke's Bay, with applicants often having high needs.