"drawing a connection" is correct and can be used in written English.
It can be used to describe the act of having an understanding between two distinct ideas, observations, or objects. For example, "By drawing a connection between their past experiences, the students were able to better understand the current social issue."
Instead, he told me it was a Don Juan serenade, and began to demonstrate, drawing a connection between Mozart's florid ornamentation and the art of flirtation.
Newspapers and magazines routinely ran stories drawing a connection between marijuana use and heinous crimes, and some people even claimed it was a cause of matricide.
Is it possible that some of Mr. Miller's messages were false in drawing a connection between spending on streetcars and Fire Department "brown outs"?
The government wants to reduce the influence of such toys on impressionable young minds, with many observers drawing a connection between juvenile war games and adult violence.
But he cannot resist joining a generation of liberals in drawing a connection between the right-wing "atmosphere of hate" in early-1960s Dandas and the assassination itself — and then linking both to today's anti-Obama zeal.
Ford's anti-Semitism has not aged well, thanks to the later excesses of its European adherents, but by drawing a connection between Christmasbashing and patriotism-scorning he pointed the way for future Christmas warriors.
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.
The first song of the day was "Thunderbolt," which draws a connection between lightning and arpeggios.
Here he drew a connection to the United States and the fighter jets it sells to Israel.
