Connecticut is an at-will employment state, and what this means is that the connection between employer and employee is very open. At any point, an employer can fire an employee for any reason; and, likewise, an employee can end their employment with a company for any reason. There are exceptions to at-will employment laws, creating chances for employees or employers to seek legal help and action if they are wronged during the termination of employment.
The most prominent exception, though, is the presence of a contract. If the employee and employer enter into a contract, this supersedes the basic rules of at-will employment. The employer can longer terminate a person's employment for any old reason; and an employee has to abide by certain standards, both professionally and personally, to maintain the contract.
This will be an important factor in Texas (an at-will employment state as well), where a Halliburton executive was recently arrested on a prostitution charge. Criminal activity is often plainly addressed in an employment contract -- if the employee is convicted of criminal activity, their employment can (and most likely will) be terminated.
Though there is no word on the employment status of the Halliburton exec yet, the current situation proves very delicate. An arrest does not necessarily activate a criminal activity clause in an employment contract. It all depends on how it is written.
For the employer, it is absolutely vital to get a legal professional with experience handling employment contract to help draft the document. For the employee, consulting an attorney in the wake of a suspected wrongful termination is just as important, if not more so. With such help, the employee's case can be fully investigated and properly handled in the court of law.
Source: Houston Business Journal, "Texas law or contract might determine Halliburton arrest response," Deon Daugherty, Oct. 17, 2012