When someone in the office loses a person close to her, it's appropriate to offer your sympathy, even though work logistics might mean that you're not close to her. The dynamics between a boss and an employee may complicate matters, but the simple gesture of sending your condolences lets her know that you understand that she may have difficulty performing at work over the next few weeks.
According to the Emily Post Institute, all offers of condolence should be in written form. Whether you are the boss or the employee, if the bereaved frequently checks email, you can send an email, but should then follow up with a card or letter. Your sympathy card needn't be extensive. Something as simple as "I'm sorry to hear of the loss of your mother" can suffice. However, if you are close to the co-worker, or if you personally knew the person who passed, it's nice to include more heartfelt words, such as sharing a favorite memory of the deceased. If you wish to do something more, you might offer some practical help, such as bringing her a favorite meal, offering to watch her kids for the evening or giving her a gift card to a local restaurant.
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