Liability question?

1) You are only liable if at fault. You'd only be at fault if it was obvious or otherwise known to you that the tree was a greater-than-normal risk, such as that it was damaged, ill, dying, or dead, or was too top-heavy, or it was leaning (e.g. the roots and soil were starting to give way), but despite knowing of that enhanced risk, you did not take reasonable steps (e.g. trimming or even cutting it down) to prevent or reduce harm. That failure to take reasonable protective action can make you liable.
But if the tree appeared healthy, etc. and you had no reason to suspect it was at a risk of falling, you would not be liable if it fell due to factors beyond your control, like a big storm.
2) Offering to reimburse a deductible does not automatically make you liable--but depending on what you say, you may provide evidence of liability. Be sure to NOT say or put in writing anything that even suggests you knew of a risk or had concerns; frame this in the context that you want to voluntarily help a neighbor. You can also see if your neighbor will sign a document that in exchange for you paying her deductible, she will give up any claims she may have had against you and indemnify (reimburse) you for any claims anyone else (like her insurer) may bring against you due to the tree.