It's not a matter to be debated. In most companies, the entire payroll is processed by the Finance & Accounts department when both are integrated. Normally and practically, it is convenient that the Payroll section also falls under Finance & Accounts. They are ideally made for each other and inseparable.
Thus, as far as employees' TDS is concerned, the Payroll section processes the payslips and provides the figures for remittance of TDS to the IT department, which is directly under Finance & Accounts. This process is also directly linked to the company's Income Tax return and hence is the primary responsibility of Finance & Accounts. It's healthier that both these operations are integrated and put under the control of one single head.
Since the Accounts section has the responsibility for IT return matters, both Form 16 & 16A authorizations for signing the forms should also be under Accounts. Moreover, the Authorized Signatory is responsible for not committing errors regarding PAN/TAN and ensuring the TDS/TCS are credited to the respective account heads. An HR Signatory cannot be insisted upon to ensure such verifications.
On the other hand, if it were under HR, the reconciliation becomes very difficult due to inadequate coordination and missing links in documentation and knowledge on IT Return matters.
Regards,
Kumar.S.