Who is legally responsible for carrying professional liability insurance coverage the employer or employee?

Neither, This is generally addressed in the terms of your employment. Sometimes the company will provide the coverage while other times The employee will.

However, Most often, when working in the employ of another the employer will carry the necessary coverage.
Neither, This is generally addressed in the terms of your employment. Sometimes the company will provide the coverage while other times The employee will.

However, Most often, when working in the employ of another the employer will carry the necessary coverage.