In general terms, Companies Act 1956 doesnt define responsibility of CS to register and record Board Minutes. However Sections 192 Companies Act 1956 defining certain resolutions (Board / General Meeting)where recording and registering is mandatory.
192. Registration of certain resolutions and agreements.
(1) A copy of every resolution [ (together with a copy of the statement of material facts annexed under section 173 to the notice of the meeting in which such resolution has been passed)] or agreement to which this section applies shall, within [ thirty] days after the passing or making thereof, be printed or typewritten and duly certified under the signature of an officer of the company and filed with the Registrar who shall record the same.
Section 192(5) which define officer in default includes Company Secretary to be responsible for recording and registering such resolutions asdefined under the said section.
As far as legal implication is concerned, Any resolution passed in Shareholders meeting which is based on board resolution (eg adopting A/c signing of balance sheet), such BR needs to be executed otherwise what is the authenticity of Shareholders resolution.
A Practicle discussion: Lets say for availing Loan, the Company needs to check its limit as per section 293(1)(d) and if limit exceed then Board needs to obtain the approval from Shareholders by passing special resolution which need to be registered in form 23 under section 192(1). how come resolution by shareholders can be passed if the same has not been passed by Board in their Board meeting without being executed in the Minutes book of Board.who will inform the shareholders in the Notice that the Company is exceeding its borrowing limits and need shareholders approval? It is the Board only which do the same by passing Board resolution and issue the notice to shareholders.Moreover Many of Banks and Financial institutuions ask for certified copy of the resolution passed by board and shareholders. In that case it is required to execute the minutes.
Companies Act 1956 is silent on the time period with which Board minutes need to be signed.