The executive branch does not, of course, pass laws regarding crime.  Laws can only be passed by the legislative branch.  However, we should not understate the role that the executive plays in creating the law.  It is often the case that the executive branch has a great deal of input into what is put in laws that are officially made by the legislature.  In addition, the executive branch can be given the authority by the legislature to write rules that, if approved, have the force of law.  This means that the executive branch can have a role in writing criminal laws even though it does not have the power to pass those laws.

The main role of the executive branch in criminal law, however, is in policing and investigating crimes.  The FBI, for example, is part of the executive branch of the federal government.  Police departments are part of the executive branches of local governments.  Prosecutors are also part of the executive branch.  These people are the ones who are most closely involved in enforcing criminal laws.

Finally, the executive branch is in charge of corrections.  People convicted of crimes enter the correctional system, which is part of the executive branch as well.  In this way, the executive branch has a role in writing laws and then is the branch that is most responsible for policing, investigations, prosecution of crimes, and punishment of convicted offenders.