Not after October 2015, if a bill passed by the legislature is signed by Governor Malloy. This bill (Read more here) prohibits employers from requiring employees to provide employers with access to personal accounts, from forcing employees to access the accounts for the employer, or from forcing an employee to allow the employer access to an online group. There is a fine associated with violating these provisions.
There are some important exceptions.
First, an employer may still have complete access to any account it maintains. So, if you have a company email address, that’s fair game. Also, a work computer or other device can also be accessed by the employer. Finally, an employer conducting certain types of investigations may be entitled to look at your personal accounts; for example, if the employer has specific information about the employee’s misconduct. This would include work related issues such as embezzlement, violations of securities law, and harassment of other employees.
Employers are also not prohibited from looking at employee’s online postings if they’re not protected. As always, be careful what you post.