BOSTON (AP) — Gov. Deval Patrick is seeking $30 million to cover the initial costs resulting from the testing scandal at a state drug lab.

The governor’s top budget official, Secretary of Administration and Finance Jay Gonzalez, said an appropriations bill would be filed with the Legislature on Thursday requesting the money.

Gonzalez says he expects the $30 million to cover costs for at least the next several months for courts, prosecutors, public defenders and other agencies that are dealing with the fallout from the drug lab crisis.

He said the money would be drawn from one-time tax and legal settlements, and if that is not enough, from the state’s so-called `rainy day’ fund.

Also Wednesday, Patrick agreed to a request by Attorney General Martha Coakley to appoint an independent investigator to look into broader issues surrounding the now-closed lab. A former chemist, Annie Dookhan, has been accused of skirting protocols and faking drug test results.