The Nova Scotia Government and General Employees Union says the workers want contract parity with those doing the same work in hospitals.
At a meeting Sunday of Local 34, the union says 97 per cent those who voted rejected the offer after conciliation talks broke down last week.
The workers provide home support for Northwood throughout Halifax.
The union says a 14-day countdown to a strike will begin on Thursday, the day after the conciliator files a report.
The union's contract expired on March 31, 2012.