From the horse's mouth and applies to anyone requiring a Russian police clearance.

Short story: My lady is from Moldova and her interview is to be in Bucharest. Having lived in Russia, she is required to produce a Russian police clearance. She went to the Moldovan Ministry of Internal Affairs to get her Moldovan clearance and at the same time have them contact their counterpart in Russia to also attain her record from there. This was possible electronically within a few days. The Moldovan Ministry then issued two certificates, stating her clear record for both the countries of Moldova and Russia.

Fast forward to Bucharest-US Embassy: They requested in a letter my lady produce a Russian clearance. We email them (for their approval) our copies of the documents issued by Ministry . They do not accept this type of clearance. They were very nice and gave us a copy of the requirement and process for the clearance to be valid. Some of the additional info may be of interest to you. Attached is a copy of this:

POLICE AND PRISON RECORDS

Available. Russian law (MVD Order no. 965, dated November 1, 2001) mandates
that the Ministry of Internal Affairs (MVD) provide police certificates both
to Russian citizens and to foreigners who have lived or are living in
Russia. The law states that in Russia, MVD offices must provide the
certificate within 30 days. Those residing outside of Russia, both Russian
citizens and non-citizens, may either delegate a Power-of-Attorney to apply
for the certificate on their behalf in Russia, or apply directly to the
Russian Consulate. Police certificates should note all names that the
person has used in Russia, and should note the MVD branches in all locations
that were queried.

Federal and more serious criminal records in Russia are kept at the Main
Information Center (MIC), while convictions related to minor offenses
(interpreted as when the punishment was to to 3 years of imprisonment) are
stored in the local police (militia) archives. Court records are generally
available upon a request from the individual. Prison records are generally
not available.

Under Russian law, a prior conviction is expunged from the MIC's databank
after a specified period of time has passed following the completion of the
sentence. For "grave" crimes the period is six years; for "especially
grave" crimes it is eight years. Thus, if an applicant committed a grave
crime and more than six years have passed since the completion of his/her
sentence, the MIC will not show a record of this crime.

In the absence of a Russian police certificate, and when dealing with
applicants who could have theoretically served prison time more than eight
years prior to the date of IV application, key features to look for are
knuckle tattoos. Russian prison culture is vibrant and unique to itself;
tattoos serve a role of establishing rank and status, and it is quite common
for males to have served time in prison to have such markings.