"No signs of deliberate destruction, demolition or damage to the monument have been found," police said in a statement Sunday.
Investigators said the 1.8-meter high statue in the Odessa region fell and broke into pieces after its decaying pedestal collapsed.
A criminal case into the destruction of the monument was opened Saturday after a local city council member told police that the statue to the Soviet leader was knocked to the ground.
Damaging or destroying historical or cultural monuments is punishable by two to five years in prison under Ukrainian law.
A number of Lenin statues across the country have been vandalized since early December amid ongoing protests against the government's decision to sideline a landmark trade deal with the European Union, opting instead for stronger ties with Russia.
One of the first and most notable acts of vandalism took place in the capital, Kiev, on Dec. 8, when a statue of Lenin was torn down by pro-European protesters in defiance of Russian influence.
Another statue of the Soviet leader was vandalized hours later in the southern town of Kotovsk.
Source: The Moscow Times