The phrase "a critical study of" is correct and usable in written English.
It can be used when discussing an analytical examination or evaluation of a particular subject, text, or phenomenon.
Example: "The book presents a critical study of modernist literature and its impact on contemporary writing."
Alternatives: "an analytical examination of" or "a thorough analysis of".
· Paul Clements is the author of a critical study of Jan Morris published by the University of Wales Press.
In 1763 Verri suggested that Beccaria next undertake a critical study of the criminal law.
Mark published on several topics, including South African literature, and in 1967 co-wrote, with Ian Gregor, a critical study of the author William Golding.
He sold her letters and wrote a critical study of her work that she detested; she excoriated him in at least two novels and a volume of autobiography.
His first experiment in the genre was Love's Comedy (published 1862), a critical study of contemporary marriage.
Paul Seydor, who wrote a critical study of Peckinpah and directed a moving Oscar-nominated documentary, "The Wild Bunch: An Album in Montage" (also contained here), has re-edited this sprawling and untidy movie, and his work is a revelation.
In still another direction: the editor of a searing (self-published) magazine of media criticism, at work on a critical study on the history of advertising.
The report was a response to a highly critical study of the program by Human Rights Watch.
Alfred Kazin made his name as a literary critic with "On Native Ground," a pathbreaking critical study of American literature.
A French Traditionalist Catholic circle has published a thorough critical study of the Harry Potter series along the lines of demonology, with the title - in English translation - Harry Potter and the Order of Darkness.
His major work, "Crabgrass Frontier" (Oxford, 1985), a largely critical study of suburbia, won the Bancroft Prize.
