My understanding, and I could be wrong, was that WW II was largely chemical free because both sides were locked in mutual deterrence.
I'm not sure about the Allies, but the Germans didn't utilize chemical weapons because Hitler absolutely forbade it. From a purely military point of view that was counter productive, but he as a gas casualty in the later part of the war and apparently this left him with a life-long horror of chemical weapons.
I read somewhere (probably on the internet so the usual caution applies), that Speer, who was opposed to the use of chemical weapons, brought in Otto Ambros (IG Farben's expert on chemical weapons) to brief Hitler on their use. This was early 1943.
Ambros told Hitler that because the allies had greater access to ethylene they could outproduce Germany in mustard gas. Hitler interrupted him saying that the older toxins were known to him but wanted specifically to know about the "new stuff" (ie Tabun and Sarin) code name "N-Stoff" and whether or not the allies had access to anything similar.
Ambros told Hitler that Farben had published research information about organophosphates and Tabun in something like 1905 (or there abouts - I can't remember exactly) and patented Tabun in 1937 and Sarin in 1938.
Ambros concluded, from the total lack of published material on organophosphates in the allies literature, that such research was top secret and therefore they were likely to have gases similar or even advanced.
In addition, it was only after the allied invasion of Normandy that Hitler became dissatisfied with the army ordnance production and testing of N-Stoff and moved responsibility for it to the SS. So testing was still going on in 44.
How much of that is true I do not know since I can't remember what the sources were or even if the sources were given.
Certainly, the use of Sarin on the Normandy beaches would have put paid to Overlord but I am not sure that the Germans had trained personnel or operational procedures in place to deploy it even if they had wanted to.
It is a interesting area of research though.
I love the smell of TOAW in the morning...