The phrase "overly relaxed" is correct and usable in written English.
It is an adjective phrase that can be used to describe someone who is more relaxed than is appropriate. For example, "The passengers on the plane felt uneasy at the overly relaxed attitude of the flight attendants."
SERVICE -- Friendly but overly relaxed.
Servers are friendly but overly relaxed.
We started to think he was overly relaxed".
Pence is the overly relaxed one who had his face permanently set to condescension.
His overly relaxed sitting posture can't have gone down well with the owner (not to mention the freakishly long legs, tracksuit/black shoes combination …)" – Matt Nicholson.
Asked if Benchmark's own investors might have the stomach to sue Benchmark, this person jokes that "every VC today could probably be sued by [their own institutional investors]" for their overly relaxed approached in dealing with startups.
In cancer cells, however, too much CHD1L can overly relax the chromatin, making the DNA vulnerable to mistake and thus raising the risk of cancer.
But for Mrs. Clinton, who is often criticized as overly scripted, her relaxed, off-the-cuff exchanges at these private events also revealed a side that she has struggled to show voters under the intense glare of a presidential race.
When the speaker is relaxed, overly emotional, dreaming, intoxicated, or joking, the unconscious is supposed to be less inhibited.
The introduction of a UI program provides an ideal opportunity to re-balance job and worker protection by relaxing overly restrictive severance pay systems, a common problem among developing countries (for international comparisons of the generosity of severance pay, see Holzmann and Vodopivec2012).
