With respect to the OP's question, it is worth noting that the EU does not impose any particular requirement on Member States for national citizenship. Since EU citizenship is derived from national citizenship (cf. Article 20 (1) of the Treaty on the Functioning of the European Union), it might be surprising, but the EU law is quite clear on that matter:
[...] in the absence of relevant Community rules, each Member State freely determines and defines the procedures for the acquisition and loss of nationality and also adopts the rules applicable to cases of dual nationality. (Case C-369/90, https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:61990CJ0369)
In short, the EU respects national decisions regarding citizenship. It is not an abuse of process for instance to be granted a particular nationality only to enjoy free movement within the EU.
In 2014, Malta introduced its Malta Individual Investor Programme (MIIP, cf. http://www.maltaimmigration.com/), recognized by the EU, that allows someone to buy his Malta citizenship (€650,000 for the main applicant), hence his European citizenship as a consequence. MIIP still accepts applications.
However, with the link provided one can see that among the requirements there is the following one:
Applicants must have a clean criminal record.
The Malta government is assumed to conduct criminal checks, and
applicants must also provide a police certificate before they will be approved for European citizenship.
The wording of this last quote is a bit strange, since in compliance with the EU law, UE citizenship is not subject to a different process than the national one. So, I guess one should understand this certificate as being mandatory for the Malta citizenship itself in the framework of MIIP.