I am sure there are a lot of varying rules regarding the use of digital cameras in the courthouses.  But, in Ohio, the Recorder cannot prohibit it.  An Attorney General's opinion in 2004 stated:

R.C. 149.43 requires a county recorder to make the public records he maintains available for inspection, without charge, to members of the public, including those who bring their own equipment to make copies of the records they inspect.

A county recorder may, for the purpose of protecting the records in his custody, maintaining the efficient operation of his office, and ensuring that other members of the public are not disturbed, adopt reasonable rules governing the use of copying equipment brought into his office by members of the public.  A recorder may not, however, absolutely bar the use of all such equipment within his office.

Best,
Robert A. Franco
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