The language on their website implies that they act collectively in the event of a veto “A vetoed bill can become law if two-thirds of the members of each house vote to override the Governor's veto.”[0].
Practically speaking, there are usually committees (may be area specific, or general such as scheduling/introductory) that make the first choice as to how the process will continue. For new york this seems to be the standing committee which decides what will be put to a vote, “ Members of Standing Committees evaluate bills and decide whether to "report" them (send them) to the Senate floor for a final decision by the full membership.”[0].
Thank you for the explanation, but that does not quite hit the spot: it explains what would happen if the governor vetoes the bill. In this case the governor claims she made some "agreement" with the Legislative to change the text of the bill shortly before signing it. And it appears that happened without Senate and Assembly voting on these changes, completely skipping this "final decision by the full membership".
I would like to know who the governor made an agreement with. The Standing Committees might be a possibility. kwiens named the bills sponsors as a possibility. (https://news.ycombinator.com/item?id=34193369). If the bill was changed shortly before signing it, i would also like to know what the text of the signed bill is. This whole process implied by memorandum #93 seems irregular to me.
Stuff like this should be documented publicly, IMHO.
