We contact them in these scenarios:
1. Dollar loss to the bank in excess of $1,000,
2. Sar characterization box "T" is checked,
3. Any other time the institution determines that the situation requires immediate (same-day) attention
Regulators second-guess that at times, but our defense is that the filing of a SAR consititutes law enforcement notification, and that the bank decides when it is necessary, not anyone or anything else.
Before adopting that stance, I called the IRS and asked if they wanted me to phone them every time we file for structuring. They were incredulous, and deferred the decision to our regulator, who deferred the decision to our institution.
Why don't we call in every case? For bank loss issues like kiting and check fraud, our local law enforcement expects an in-person visit at their office, for a report to be completed, and this is undesirable and time-consuming.
Does it depend on your relationship with LE? Absolutely. Some regional SAR coordinators are more on the ball than others.
What do you give them? The information described in the SAR can be verbally reported to them over the phone, when possible, and it is covered by Safe Harbor. If they are not interested, they tell me "Thank you." If they are interested, they used to ask for a copy of the SAR to be sent to them directly, in addition to the copy filed with FinCEN. Nowadays we just tell them one business day after it is filed, that it is now available for them to download. We don't care for faxing copies around.
"It is natural to give a clear view of the world after accepting the idea that it must be clear." - Albert Camus