Seattle requires adjoining landowners to maintain the sidewalks adjacent to their property. Seattle has a program to deal specifically with sidewalk repair; in some circumstances the landowner may need to pay for the repairs. In the event of an injury to a third party, the landowner is only liable if they have done something to cause the (unsafe) condition, which includes allowing nearby tree roots (from a tree planted by the owner) to push up the sidewalk. Not all cracks on a sidewalk will be considered “unsafe” or “dangerous”. It is a case-by-case analysis and may depend many different factors. In most situations, it is most likely a “I know it when I see it” test.
Maintaining the vegetation on your property to minimize impact on the sidewalk would be prudent. Avoid planting trees with shallow roots near the sidewalk. The city remains liable if the sidewalk is not reasonably safe for ordinary use – and it has notice, constructive or actual, of the condition. A good resource for landowners in Seattle and their rights and duties is: