If anyone came close to creating a death ray weapon by the end of the Second World War, it was the Japanese army. It wouldn't have helped them much, however, as they weren't at war with rabbits. According to Richard Overy in The Air War 1939-1945 (Washington: Potomac Books, 2005 ), 195:
The lack of satisfactory evaluative machinery led for example to the diversion of considerable resources to the search for a 'death ray'; a search that Western powers had abandoned in the 1930s. By the end of the war the Japanese 'ray' could kill a rabbit after five minutes at a distance of 1,000 yards.
The reference Overy gives for this is the U.S. Strategic Bombing Survey, report 15, appendix XX, but this appears to be in error as that's online and has only ten appendices. According to this site, report 63 (Japanese Air Weapons and Tactics) does in fact discuss the death ray. Unfortunately I can't find that one (not for free, any way).
But there are a few more snippets to be found online. This is from Radar Origins Worldwide: History of Its Evolution in 13 Nations Through World War II (Trafford Publishing, 2009) by Raymond C. Watson Jr, 334-5:
The Ku-go (Death Ray) was another matter. An Article on a death-ray device invented by Nikola Tesla had been in The New York Times (July 11, 1934), and was picked up by the Japanese press. In this, Tesla was quoted as saying that his beam would "drop an army in its tracks and bring down squadrons of airplanes 250 miles away." Magnetron research at the NTRI and JRC appeared to indicate that a beam device with tremendous output power might be possible.
In 1943, work began at the Shimada City research facility on developing a high-power magnetron that, if not as capable as Tesla had boasted, could at least incapacitate an aircraft. A number of Japan's leading physicists were involved in this activity, including Sin-Itiro Tomonaga, another future Nobel laureate. By the end of the war, their effort had produced a 20-cm magnetron with a continuous output of 100 kW, far short of the desired 500 kW, which itself would likely have been insufficient for the mission. Like other Project Z efforts, documentation was totally destroyed before Japan surrendered.
It looks like there is much more in Walter E. Grunden's Secret Weapons and World War II: Japan in the Shadow of Big Science (Lawrence: University of Kansas Press, 2005), but I can only see a few of the relevant pages online. (There's also a lengthy review at Stone & Stone Second World War Books.) According to Grunden, the Japanese army (by way of the Army Institute of Scientific Research) first looked into death rays in 1930, again inspired by a newspaper article -- this time claiming that Germany had invented an 'electric wave' weapon in the First World War. The main application envisaged was air defence, but it could also be useful for coastal defence. It was concluded then that the necessary energy output was impossible with available technology, but later in the decade improvements in magnetrons made a death ray seem more feasible. As far as the actual experimental research is concerned, Grunden says the following (110-1):
Research toward developing a weapon utilizing microwaves began [at the Noborito laboratory of the AISR] around 1939 on a small scale with a team of thirty technicians. Their objectives were to determine how best to generate microwaves and how to stop an internal combustion engine by the resonance effect, and they sought to conduct basic research on the physiological effects of microwaves on live animals.
That's about all I can find (well, all that has any supporting references at all). Obviously Ku-go never was never a practical weapon, but it sounds like the Japanese army got closer to it than Grindell Matthews did, or Tesla for that matter.
Overy places Japan's death ray research in the context of wasteful research projects, arguing that both the Axis powers made poor choices as to research projects (V-2 rockets being another one). That's a bit too strong a conclusion; in research some alleyways will turn out to be blind, and anyway the Allies made some poor choices too (Lindemann's parachute mines, for example). And there was no guarantee that the Manhattan Project would result in a working atom bomb, in which case it would have been the most expensive white elephant ever. But the point is, as Overy also notes, that the Allies had the scientific resources to spare on possible dead ends, whereas Japan and (to a lesser extent) Germany did not. It's another part of the reason why the Allies won.