Index Match Function Multiple Values

I am attempting to use the Index Match function to separate data, by State, into new worksheets. The goal is to have any changes made to Sheet 1 occur across all other sheets. I can do this if I am simple replicating the data, however, when I want to only include "Connecticut" in Sheet 3 (CT) or "Rhode Island in Sheet 4 (RI) it works, but the unmatched data causes unwanted information.

The problem is this: Index Match reviews all Rows, so if it does not match, the result is a "#N/A", is there any way to index only the matching name "Connecticut" and ingnore the rest.
Also, for Rhode Island, it replicates the first match for every row that is unmatched until it reachs a match... you can see this in Sheet 4. Barrington repeats.

How can I use the Index Match or other functions to pull data for only one State per sheet.

Excel Function Help.xlsx

Hi Miketron - Appreciate the suggestion but that would not work for what I am trying to do. You see, the first sheet is the control document. To elaborate, say I add a new city in Connecticut to the first sheet. I need that new line to update automatically in sheet "CT". When I say automatically, I mean by pulling the formula down and over on all the cells in the sheet "CT". Does that make sense?

Using a pivot table would work but I would have to redo the pivot table every time I updated the control sheet, and that is not what we are trying to accomplish