For most homeowners, the answer is no. The 41.5 Covenants have specific language about this that should be reviewed and by contacting the VP/Architecture board official. The City of Bellevue official document on tree removal is here
From a Bellevue City perspective, a permit may be required if one or more of the following conditions is true:

• Tree removal results in more than 1000 square feet of disturbance of the ground.
• the property is part of a designamted critical area or buffer.
• The tree is in a native growth protection area or a retained vegetation area.
• The tree is on the city's right of way adjacent to your property

Contact the Land Use desk in Development Services (425-452-4188) or landusereview@bellevuewa.gov for assistance in determining whether you need a permit.