I believe that in English "responsibility" or "liability" would be used in this context more than "compliance".

Regulatory compliance is an organization's adherence to laws, regulations, guidelines and specifications relevant to its business. Violations of regulatory compliance regulations often result in legal punishment, including federal fines.
What is regulatory compliance? - Definition from WhatIs.com

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Note added at 5 hrs (2017-11-13 21:44:17 GMT)
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This is the term in business, and it covers,as the definitions clearly state, adherence to laws. This means that if you break the law, there are penalties for doing so, as a crime has been committed. The term is quite clear as to what it involves, "Criminal compliance" much less so.

Regulatory compliance
From Wikipedia, the free encyclopedia

In general, compliance means conforming to a rule, such as a specification, policy, standard or law. Regulatory compliance describes the goal that organizations aspire to achieve in their efforts to ensure that they are aware of and take steps to comply with relevant laws, polices, and regulations.[1] Due to the increasing number of regulations and need for operational transparency, organizations are increasingly adopting the use of consolidated and harmonized sets of compliance controls.[2] This approach is used to ensure that all necessary governance requirements can be met without the unnecessary duplication of effort and activity from resources.

I'm assuming this refers to what is called in Spain "compliance penal" or "(corporate) criminal compliance" (= "implantación de sistemas de control de cumplimiento normativo y prevención del delito". Here are some references:

http://www.taglaw.com/government-investigations-a-white-coll...

http://language.hoganlovells.com/files/Publication/4f7c9c3c-...

http://www.cuatrecasas.com/es/areas_de_practica/corporate_co...


http://perezdomingo.com/en/servicio/corporate-compliance-2/



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Note added at 2 hrs (2017-11-13 19:12:07 GMT)
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Certain Spanish corporations must have a "sistema de compliance penal" and a "compliance officer"
http://www.kpmgcumplimientolegal.es/estandar-nacional-compli...

Las Leyes Orgánicas 5/2010 y 15/2015, de modificación del Código Penal, han introducido, respectivamente, los requisitos para la atribución de la responsabilidad penal de las personas jurídicas y el régimen legal para la exención de dicha responsabilidad. Esta exención es posible siempre que la empresa cuente con un eficaz programa de prevención de delitos.
Además, la vigencia de este régimen legal de responsabilidad penal para las empresas y la posibilidad de eximirse de la misma, solo en el caso de que los programas de prevención hayan sido real y eficazmente implantados, ha sido confirmada tanto por la Circular 1/2016 de la Fiscalía General del Estado como por las Sentencias 154/2016 y 221/2016 de la Sala de lo Penal del Tribunal Supremo.
En la medida en que a todas las empresas afecta el régimen de responsabilidad penal, es casi necesario que las empresas deban diseñar e implantar sistemas y políticas corporativas de prevención de comportamientos delictivos en la empresa y por ello la figura profesionalizada del Compliance Officer, responsable del cumplimiento del marco regulatorio y normativo en el ámbito penal que afecta a las empresas, resulta de suma importancia dentro de la organización.

http://www.abogacia.es/2017/03/16/curso-compliance-officer/



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Note added at 16 hrs (2017-11-14 09:02:47 GMT)
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Hi, I understand your concern, but the audience for your translation will most likely understand what is meant. (Anyone involved with corporate management certainly will.)

"Corporate criminal compliance" is short for "compliance program/system to prevent and detect corporate crime",(i.e., bribery, tax fraud, money laundering, competition law violations, etc.,). By law, certain corporations must have a compliance program with a compliance unit and a compliance officer, etc. As an example, here is how the German vehicle manufacturer MAN describes its compliance program:

MAN’s Compliance Program focuses on white collar crime (especially anticorruption, prevention of money laundering) and antitrust law. In this respect, MAN has developed a Group-wide Integrity and Compliance Program that:

prevents compliance violations (prevention),

detects as early as possible any compliance violations that may arise despite preventative measures (detection), and

responds quickly and efficiently to these compliance violations (response).

Corruption and cartel formation pose particularly high risks for the Company and its employees. Compliance violations in these areas can lead to high fines for the Company, penal sanctions against employees, actions for damages brought by customers, competitors and suppliers, order freezes and negative press.

MAN’s Supervisory and Executive Boards have also pushed to improve the compliance system as a result of the investigations following allegations of corruption, so that such cases do not occur again under any circumstances.

https://www.corporate.man.eu/en/risk-and-compliance/man-comp...