Employer Salary Reduction Rules

Summary

Employers in Connecticut can reduce wages if they notify employees in advance and ensure wages do not fall below the minimum wage. Adjustments due to benefits are permissible but must comply with these rules. If you feel unfairly treated, consider discussing with HR or a labor attorney.

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But can they reduce it because I am going on their insurance
In Connecticut, an employer can adjust wages due to changes in benefits, but they must inform you in advance. However, if this results in a wage less than the minimum or discrimination, it could be problematic.
How is that fair
Fairness can be subjective. However, legally, as long as the employer follows the rules such as notifying you in advance and not reducing wage below minimum, it's permissible. If you feel unfairly treated, consider discussing with HR or a labor attorney.