playing mixed events
Yes, there is an addition adjustment that must be made in mixed events where two or more tees are in play (different course ratings - men vs. women, men vs. men, women vs. women) if there is a difference in par values. This is Rule of Handicapping 6.2b, and is an important application in the interest of fair play.
First, the players convert their respective Handicap Indexes to Course Handicaps based on the Slope Rating of tees being played. If there is a difference in par values between the tees / ratings, the extra strokes must be accounted for by either adding the strokes to the players playing the higher par, or subtracting strokes from the players playing the lower par. For example, if the White tees for Men is par 71 and the Red tees for Women is par 72, this represents a one stroke difference. The Competition Committee can either reduce the Playing Handicaps of the Men by one stroke, or can add one stroke to the Women's Playing Handicaps.
Keep in mind that ratings have a gender, tees do not. For example, you could have Men and Women both playing from the White tees, which could be par 72 for Men and par 73 for Women. It's also important to note to not rely on a scorecard for Course Rating / Par information, which could be outdated - rather, be sure to check Course Ratings in GHIN.
If there is no difference in par values between the tees / ratings, there is no additional adjustment necessary.