Looks like it is not a choice for the pilots to give a statement after an accident if requested by NTSB
a)
Reports. The operator of a civil, public (as specified in
§ 830.5), or foreign aircraft shall file a report on Board Form 6120. 1⁄2 (OMB No. 3147-0001)[<a href="#830.15-footnote-2" data-turbo="false">2</a>] within 10 days after an accident, or after 7 days if an overdue aircraft is still missing. A report on an incident for which immediate notification is required by
§ 830.5(a) shall be filed only as requested by an authorized representative of the Board.
(b)
Crewmember statement. Each crewmember, if physically able at the time the report is submitted, shall attach a statement setting forth the facts, conditions, and circumstances relating to the accident or incident as they appear to him. If the crewmember is incapacitated, he shall submit the statement as soon as he is physically able.