The first attack came shortly after midnight, when unidentified assailants opened fire on a car belonging to an Ingush lawmaker, Ruslan Gagiyev. His brother, who was at the wheel, was critically injured and died in intensive care.
"Gagiyev himself was not in the car," the source told RIA Novosti.
About half an hour after the first attack, gunmen shot at a traffic police post in the city, injuring an officer. Ten minutes later a police station in the city came under fire, apparently from the same gunmen, and one person was injured.
The local Interior Ministry confirmed the attacks but did not give further details.
Sporadic terrorist attacks and militant clashes remain common in Russia's North Caucasus republics, although the active phase of the Kremlin campaign to fight separatists and terrorists in Chechnya is over. Violence often spills over into neighboring republics, in particular Ingushetia and Daghestan.