If we are closing an account due to overdrafts, are we allowed to pull the funds from another account they have with our institution? Example,if they have a sole owner account that we closed but a joint account with sufficient funds to cover? Just wondering what other banks might do in this situation.

if we see a history of moving funds between the two accounts then we offset

Your deposit agreement should cover this. If it says you will, then you're fine to offset against another account of the same owner (including joint account).

agree with Brenda, check your deposit agreement with the customer...

You may wish to google Right to offset for your state to verify if there are any state issues but it is usually a common transaction as stated above.