The chairman of the House Judiciary Committee has asked President Reagan and Attorney General William French Smith for copies of all records concerning the preconfirmation investigation of Secretary of Labor Raymond J. Donovan.

Chairman Peter W. Rodino Jr. (D-N.J.) said he was seeking the documents as a result of a resolution of inquiry introduced by Rep. Toby Moffett (D-Conn.) and sent to Rodino's committee last week.

Rodino emphasized that he is concerned primarily in the "serious questions about the entire process of executive branch background investigations" that the Donovan case raises.

He said in a statement that his committee would take "a close look" at several issues, including:

* "The completeness and accuracy of FBI background checks on high government officials.

* "The relationship between the FBI and the White House in these matters.

* "The difficulties that the FBI encounters within its own organization in retrieving information on people under investigation."

The Senate approved Donovan's nomination on Feb. 3, 1981, after controversial confirmation hearings concerning charges of union corruption and alleged links between Donovan and his New Jersey construction company and organized-crime figures in New York and New Jersey.

Donovan has denied any wrongdoing or impropriety.

Rodino said he is interested in the broad issues of "how information is supplied to the FBI and then to the Senate in these background investigations, and . . . whether there are any flaws that could lead to information gaps or possible improprieties by executive branch officials."

Rodino's aide said the congressman asked for quick responses in light of the privileged nature of a resolution of inquiry. Moffett can call it up on the House floor unless the Judiciary Committee acts within the next week.