This response is for education purposes only and is not intended to be legal advice or establish an attorney client relationship.
Based on your question it appears that you are concerned about liability if a worker gets hurt on your property. If a worker gets hurt on your property because of an unreasonably safe condition or defect on your property, you may be liable under a premises liability theory even if the tree company has worker's compensation insurance.
Regarding the indemnity certificate, you would have to look at the language of the certificate to determine the scope of indemnity.
I hope this helps - good luck
this question was asked a long time ago, but since it addresses one of my "pet peeves" let me answer by saying that it should be a requirement for a tree removal company to carry workers' compensation for its employees because this is a very dangerous job and without insurance, the workers' are often thrown to the curb and have little recourse for serious and expensive medical needs. By contributing to the problem in supporting uninsured contractors, you are perpetuating a dangerous situation. it is unlikely that only the contractor you hired will be doing all the work and if his helper is injured, he may come looking to your homeowners' insurance to cover the tab. While liability may be tough to prove, why would you want to expose yourself to any liability?