"INITIAL CLASSIFICATION OF THE CRIME/OFFENCE” is the phrase commonly used in the case-law of the European Court of Human Rights and in legal publications.
I've also found some Google hits for “initial legal classification” (see below).

1. The word for “КЛАССИФИКАЦИЯ” is usually translated as “CLASSIFICATION”.

See, for instance:

Criminal procedure sets forth different rules that govern courts, defendants, and law enforcement agents depending on the crime's classification…
Implications of a CRIME'S CLASSIFICATION - FindLaw
criminal.lawyers.com › Criminal Law › The Criminal Law Process

Crimes are usually CLASSIFIED as treason, felony, or misdemeanor. The fundamental distinction between felonies and misdemeanors rests with the penalty and the power of imprisonment. In general, a misdemeanor is an offense for which a punishment other than death or imprisonment in the state prison is prescribed by law.
criminal law: Classification of Crimes - Infoplease
www.infoplease.com/encyclopedia/society/criminal-law-classi...

Criminal Offences can be classified as summary, either way or indictable only offences and this classification determines how a case is processed through the criminal justice system.
www.lawteacher.net › Law Help › Lpc › Criminal Litigation [the UK]

Grand Chamber hearing concerning reopening of criminal proceedings in respect of offences newly CLASSIFIED as war crimes.
hudoc.echr.coe.int/webservices/content/pdf/003-4413848-5303556?TID

During the trial, if the LEGAL CLASSIFICATION of the crime is considered incorrect, the court must discuss the new CLASSIFICATION. If new facts are revealed related to the crime charged, the court can change the charges and try the crime as such. If, during the proceedings, new facts are revealed which may constitute another crime, connected to the one charged, the court can request the addition of new charges. The court will decide whether to add new charges or refer the case to the police or prosecution for further investigation.
https://e-justice.europa.eu/content_rights_of_defendants_in_...

… In a decision given on 28 January 2003, the Bucharest Court of Appeal dismissed the applicant’s arguments concerning the LEGAL CLASSIFICATION of the crime he had committed, endorsing the reasons given by the first-instance court on that point
hudoc.echr.coe.int/webservices/content/pdf/001-118740?TID=ihgdqbxnfi


2. For "INITIAL CLASSIFICATION” (of the crime/offence), see e.g.:

Human Rights and Criminal Procedure: The Case Law of the European ...
https://books.google.com.ua/books?isbn=9287166897
Jeremy McBride - 2009 - ‎Law
These circumstances give rise to strong suspicion as to the existence of an ulterior purpose in the INITIAL CLASSIFICATION OF THE OFFENCE.

The division between the magistrates court and the Crown Court will be by the INITIAL CLASSIFICATION OF THE OFFENCE as either being summary giving exclusive jurisdiction to the magistrates court or of indictable offences giving exclusive jurisdiction to the Crown Court
the agencies of the criminal justice system - UK Essays
https://www.ukessays.com/.../the-agencies-of-the-criminal-ju... [the UK]

... [T]he initial classification should have been recorded as CRI until an offence was confirmed as opposed to an INITIAL CLASSIFICATION OF CRIME subsequently being altered to reflect No Crime confirmation. …
In order to reduce the number of initial classification of offences being amended to No Crime an action plan has been implemented on the borough
policeauthority.org/Metropolitan/dsvb/2010/101116/01c/index.html [the UK]

Crime Bureau Policy (Harmonised) - West Mercia Police
The INITIAL CLASSIFICATION OF THE CRIME and the number of crimes recorded will be determined and validated by the Crime Decision Makers
https://www.westmercia.police.uk/media/.../Crime_Bureau_Poli... [the UK]


3. For “initial legal classification”, see:

Criminal Justice - Page xxxiii - Google Books Result
Andrew Sanders, ‎Richard Young, ‎Mandy Burton - 2010 - ‎Law
... the Crown Court is determined by the INITIAL LEGAL CLASSIFICATION of an offence as either 'summary' (triable in the magistrates' courts only) …
https://books.google.com.ua/books?isbn=0199541310



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Note added at 10 hrs (2017-01-28 19:42:15 GMT)
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Correction:
I mean the translation of the word “КЛАССИФИКАЦИЯ” in this particular context.