Air carrier landing RIC experienced TCAS RA descending from 14;000 FT with unreported traffic.

Narrative

Flight from ZZZ to RIC. While descending 14;000 FT through 8;000 FT under the control of Approach; approximately 30 NM east of Hopewell VOR (HPW) on an IFR flight plan; Captain and First Officer noticed an aircraft on TCAS; and closing. Our TCAS issued a TA; 'Traffic; Traffic' along with an orange visual indication on the MFD. Captain was pilot flying; and First Officer was pilot not flying. Shortly after; ATC issued instruction; 'Turn left immediately 180!' Captain turned autopilot off and began an immediate left turn to remain clear of the traffic; and continued to descend as previously instructed by ATC. Very shortly after; our TCAS issued a climbing RA; 'Traffic; Traffic; Climb' along with a red visual indication on the MFD. A green climb vector also appeared on VSI. These indications were in direct conflict to what Approach instructed us to do; so I told Approach that we had a TCAS; and that we were climbing! Captain transitioned to a climb; and continued the left turn to 180 degrees. The traffic was never seen visually; we were in mixed IMC and VMC. Separation displayed on MFD; less than 1;000 FT vertically and les than 2 miles laterally. Once 'Clear of Conflict' message was issued; I queried Approach several times as to a heading and altitude to return to. ATC issued a heading and a continued descent down to 6;000 FT. Captain complied with these instructions. ATC issued a frequency change shortly after to Richmond Approach.