WASHINGTON—Attorneys for the woman who accused Brett Kavanaugh of sexual assault said she wants a full investigation of the allegations before she testifies on Capitol Hill, throwing into doubt a planned Monday hearing that would have pitted her word against that of the Supreme Court nominee.

In a letter Tuesday to Judiciary Committee Chairman Chuck Grassley (R., Iowa), attorneys for California college professor Christine Blasey Ford asked for “a full investigation by law-enforcement officials” to “ensure that the crucial...