AP Stylebook entry
that (conjunction) Use the conjunction that to introduce a dependent clause if the sentence sounds or looks awkward without it. There are no hard-and-fast rules, but in general:
–That usually may be omitted when a dependent clause immediately follows a form of the verb to say: The president said he had signed the bill.
–That should be used when a time element intervenes between the verb and the dependent clause: The president said Monday that he had signed the bill.
–That usually is necessary after some verbs. They include: advocate, assert, contend, declare, estimate, make clear, point out, propose and state.
–That is required before subordinate clauses beginning with conjunctions such as after, although, because, before, in addition to, until and while: Haldeman said that after he learned of Nixon’s intention to resign, he sought pardons for all connected with Watergate.
When in doubt, include that. Omission can hurt. Inclusion never does.