Yes, according to the US translated version of the ki-61 flight manual 「キ61操縦法」, the official dive limit was 700 kph IAS. Unfortunately, it seems both ki-61’s original flight manual and operation manual in Japanese may have been lost, since it does not appear in the market.
You might have seen some Japanese aerospace magazines list ki-61’s dive speed limit to be 850kph, that number is definitely too high, presumably derived from static load data that does not reflect aeroelastic and compressibility that airframe will meet at critical Mach number. As there are even few US aircraft like P-51 and P-47 were hardly allowed to perform a dive at that high speed. The reason was compressibility, the airflow will separate at high speed, causing the aircraft to experience buffet/flutter/stall/control reversal. Some pilot may claim to perform a dive higher than this speed, either they had enough experience to recover from a compressibility dive, or the pitot static tube shows incorrect data at critical mach number ( sometimes off by 100 knots). N1K2 was designed to perform 450 knots IAS dive, but in reality the number was limited back to 400 knots due to unsolved compressibility shock wave issue.
Furthermore, Ki-61 airframe does not show any property to support it to dive at 850kph, yes it has tri-spar design. But don’t forget that ki-43 too used tri-spar and proved to be structurally weak. Ki-61’s airfoil was quite conventional with a quite convex mean chamber line at leading edge (NACA 24000), a large aspect ratio of 7.2 , and with a large aileron span( about 50% of wing span). All of those properties means it will have a quite low critical mach number (airfoil cause early separation), a larger AR ratio results in earlier separation on the wing tip further reducing its critical mach number, and its large ailerons would likely encounter heavy flutter due to aeroelastic effect at this compressibility dive.
The policy of War Thunder on dive speed limit is usually said to be +30kph on the number displayed in official flight manual, thus we see quite low dive speed limit on soviet planes.