As a pedant, I suggest that the managing agent is not disinterested, even if they are uninterested. Perhaps you need to point out the distinction to them! However, the responsibility ultimately lands with the committee, unless over-ruled but a decision of a general meeting.
If the carpark is common property, and exclusive use of part of the common property is being given to one owner, then there is certainly a process required for that. The details of the process and who can exercise it depend on the state. If it is not a ‘minor use’ of common property, it requires a general meeting resolution anywhere.