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[CONRAIL LOGO]
 
                                                                 EXHIBIT (a)(32)
 
                                                                   March 7, 1997
 
Dear Shareholders:
 
     Conrail Inc. and CSX Corporation have agreed to modify our merger agreement
to provide that Conrail shareholders will receive $115 in cash for each
outstanding share of Conrail common stock and ESOP preferred stock. Pursuant to
the amended agreement, CSX will amend its tender offer to offer to pay $115 in
cash for each outstanding share, and will provide that the tender offer will
expire no later than June 2, 1997. Following consummation of the CSX tender
offer, CSX will consummate the merger in which Conrail's shareholders will
receive $115 in cash for each remaining Conrail share.
 
     Our amended merger agreement provides unprecedented value to Conrail
shareholders and provides that they will be paid in under 90 days without
regulatory risk. We have also worked to fully protect the Conrail employees who
have made this railroad great. Stay bonuses and enhanced severance arrangements
have been implemented to protect those Conrail employees not covered by
collective bargaining agreements. In addition, we have received assurances from
CSX that there will be a substantial commitment to Pennsylvania. CSX intends to
have a major operating presence in Philadelphia and intends to maintain
Conrail's Pittsburgh service center and the shops at Altoona and Hollidaysburg.
 
     Conrail's board and management would have preferred for the Conrail system
to remain intact. However, under the circumstances as they developed, we have
succeeded in negotiating the best possible transaction for all of Conrail's
constituencies.
 
     Under the amended agreement, senior members of Conrail and CSX will lead a
team to ensure an orderly process throughout the transition period. Three of
Conrail's directors will also be invited to join the CSX board.
 
     It is anticipated that CSX and Norfolk Southern will negotiate an
appropriate division of Conrail's assets; however, the CSX-Conrail amended
agreement is not conditioned upon CSX reaching agreement with Norfolk Southern
nor is it subject to financing.
 
     YOUR BOARD OF DIRECTORS HAS UNANIMOUSLY APPROVED THE CSX TENDER OFFER AND
MERGER AND RECOMMENDS THAT CONRAIL SHAREHOLDERS ACCEPT THE CSX TENDER OFFER AND
TENDER THEIR SHARES IN SUCH OFFER.
 
     The enclosed Supplement to the Offer to Purchase prepared by CSX and the
Amendment to the Schedule 14D-9 prepared by Conrail describe the terms of the
revised CSX tender offer. I urge you to consider all such information carefully.
 
                                          Sincerely,
 
                                          /s/ David M. LeVan
                                          DAVID M. LEVAN
                                          Chairman, President and
                                          Chief Executive Officer