"draws a connection" is correct and can be used in written English.
You can use it when you want to express that some kind of relationship or similarity between two or more things has been recognized. For example, "The author draws a connection between the behavior of animals and the behavior of humans."
The first song of the day was "Thunderbolt," which draws a connection between lightning and arpeggios.
Todd Boyd, an expert on race and popular culture at the University of Southern California, draws a connection between the stereotypes of black people perpetrated by Hollywood in the days of legal segregation and Perry's caricatures.
Mr. Krakauer draws a connection between the revelations the Lafferty brothers claimed guided them and early Mormon acts of "blood atonement," in which followers targeted victims because of purported divine inspiration.
Mr. Simmons, for his part, draws a connection between the apparent decline in the mixtape circuit and this year's sharp drop in rap sales — more than 20percentt, far more than the 15percentt slide in album sales over all.
He was a keen Darwinian, and so he asks us to consider the kind of evolutionary explanation for religion that argues it has some survival advantage, or that draws a connection between, say, religious emotions and sexual life.
Last year's follow-up, Life and Death..., sheds even more light on the US's political and institutional failings, and draws a connection between Aileen's awful childhood and her delusional state prior to her execution.
She also, inadvertently, drew a connection to Ms. Schapiro.
But Ken Dulaney, an analyst with Gartner, drew a connection between the departures of the Microsoft and Intel executives.
He then drew a connection between his student days and his current situation.
Here he drew a connection to the United States and the fighter jets it sells to Israel.
In his sermon, Dr. Johns drew a connection between the chasm and segregation.
