The Social Protection Minister says the Government should examine the possibility of introducing "Clare's Law" here.
The legislation comes into force in England and Wales today - allowing people to check with police if their partner has a history of domestic violence.
The law's named after Clare Wood from Manchester.
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In 2009, she was murdered by her ex-boyfriend, who unbeknown to her, had a history of violence to women.
Speaking on International Women's Day, Minister Joan Burton says the Government needs to consider this law - as a means to tackling domestic violence.