According to the official Chinese narrative, Lin was planning to topple Mao with Soviet military help. When this failed, he tried to escape to the USSR.
Did the Soviets bother to respond to these accusations? What did they say?
There does not seem to have been any official response. As discussed by historian Qiu Jin (see pp. 195-196), there is essentially no evidence to support the official Chinese accusation that actually Lin Biao intended to flee to the USSR. They presumably saw little reason to respond to the baseless accusation given the larger context of Sino-Soviet relations at the time.
The Wikipedia article on Lin Biao does describe a secret Soviet investigation which tentatively identified one of the bodies at the crash site as Biao. But only a few Soviet officials were informed of this and it remained a secret until the 1990s.
EDIT: Another key detail from the Wikipedia article actually suggests that Soviet officials did deny Lin Biao was heading to the USSR:
Lin's plane initially traveled southeast (in the direction of Guangzhou). The plane then returned twenty minutes later and circled the airport several times as if it were trying to land, but the runway lights had been turned off. Soviet officials and Mongolian witnesses reported that the plane then flew north, over Mongolia and almost to the Soviet border, but then turned around and began flying south before it crashed.