Do I owe any obligations to the insurance company concerning my claim?

Yes. Decisions from the courts in many states indicate that the you (the insured) have a reciprocal obligation to act fairly and deal in good faith. This would include your 

(1) timely submitting your claim for benefits (bearing in mind that most policies state when a claim must be submitted after a loss has occurred), 

(2) providing all information that the insurer reasonably asks for (if it is entitled to it under the policy or the law), 

(3) giving a statement under oath concerning the claimed loss (again, if the policy so requires - as many policies do), and 

(4) generally cooperating with the insurer regarding the loss (like allowing it to inspect the damaged property in case of a damage claim, for example, a claim after a flood or fire).