The investigation into Chris Cook's Saturday morning arrest has yet to be completed. Eden Prairie Police continue to look into the incident that wound up with Cook being detained and held without bail while facing multiple domestic assault charges.

Cook was originally scheduled to appear before a judge Monday morning but that hearing has now been pushed back until Tuesday.
Still, regardless of what happens with the legal proceedings of Cook's case, he is almost certain to face punishment from the NFL for being in violation of the league's personal conduct policy. As to whether Cook can be labeled a repeat offender by the league? That's a gray area. His March arrest in Lynchburg, Va., for pulling out a gun during a verbal altercation with a neighbor came during the NFL lockout when the league had no direct oversight of the players. Neither the collective bargaining agreement nor the personal conduct policy were in effect.

(Cook was later found not guilty on the gun charge.)
As for how the NFL will handle Cook's most recent transgression, one which includes allegations of domestic assault and strangulation, you can bet it won't be taken lightly. Greg Aiello, the NFL's senior vice president of public relations, told the Star Tribune on Monday that the league has yet to discuss punishment for Cook but will review the matter.
A passage from the personal conduct policy reads as follows:

It is not enough simply to avoid being found guilty of a crime. Instead, as an employee of the NFL or a member club, you are held to a higher standard and expected to conduct yourself in a way that is responsible, promotes the values upon which the League is based, and is lawful. Persons who fail to live up to this standard of conduct are guilty of conduct detrimental and subject to discipline, even where the conduct itself does not result in conviction of a crime.

When it comes time for the NFL and commisioner Roger Goodell to issue a ruling on Cook, they will consider everything from fines to suspension to a potential probationary period.

The disciplinary response will be based on the nature of the incident, the actual or threatened risk to the participant and others, any prior or additional misconduct (whether or not criminal charges were filed), and other relevant factors. … With respect to repeat offenders, the Commissioner may impose discipline on an enhanced and/or expedited basis. In such cases, the timing and nature of the discipline will be determined by the Commissioner based on several factors including but not limited to: the severity of the initial charge and later charge; the facts underlying the later charge; the length of time between the initial offense and later charge; and the player or employee's compliance with counseling and other programs.

In addition to any punishment Cook receives, he will also likely undergo a clinical evaluation. More from the personal conduct policy:

Based on the results of that evaluation, the person may be encouraged or required to participate in an education program, counseling or other treatment deemed appropriate by health professionals. The evaluation and any resulting counseling or treatment are designed to provide assistance and are not considered discipline; however, the failure to comply with this portion of the Policy shall itself constitute a separate and independent basis for discipline.