Hello,
Indeed, the deduction of the impôt à la source must be on the payslip. Do you remember if you filled up a formular where you declared civil status (married, not married) , number of children, religion? They need this info to estimate your tax amount.
There's another important document called certificat de salair/lohnausweiss, this is an example of the document
https://www.estv.admin.ch/dam/estv/f...rechts-dfi.pdf
Field number 12 in the certificat the salaire is impôt à la source. If this document says they deducted the tax, there might not be a problem in first place, just a confusion in the HR department.
But, 3000 CHF seems low for 16 months at 80K annual. You might be liable for more, check what should have been the tax according to civil status, etc. I guess HR applied the wrong barème and they're just applying the correction
https://www.vd.ch/themes/etat-droit-...emes/#c2025841