The trio, who wore fluorescent jackets and face coverings, entered Halifax Bank in Southgate at 4.30pm.
It is believed that they were armed with a crowbar and sledgehammers, which they used to threaten staff and cause damage inside the bank.
They fled the scene in a black vehicle when they failed to get any money.
West Yorkshire Police today issued an appeal for any mobile phone footage of the incident.
Detective Chief Inspector Chris Gibson, of Calderdale CID, said: "I would appeal for anyone who saw this to get in contact. It was at a busy time of the day and we believe members of the public filmed the incident on mobile phones.
"We are particularly appealing for those people to come forward.
"Thankfully incidents like this are rare in Calderdale and I understand that the incident will have caused concern in the community. We have increased patrols of high visible, uniformed officers in the area to offer reassurance."
Call Calderdale CID on 101, quoting crime reference 13170016586.