Boston Heart Diagnostics Corp. must defend a False Claims Act case alleging it paid kickbacks to secure lab test referrals.

The Boston-based diagnostic lab group can’t evade claims that it waived copays or patient deductibles from doctors’ privately insured patients so the doctors would send the company their lipid tests.

The court agreed with the company that certain allegations had to be dismissed but said the company will have to defend claims that it paid inflated packaging fees to induce...