Do I need to supplement Vitamin D if I drink fortified milk?

It depends...

Possibly.

The Recommended Dietary Allowance (RDA) for Vitamin D is currently set at 600–800 IU/day (15–20 mcg) for adults. Fortified milk typically provides 100 IU per 8 oz serving (236 mL).[1] So while milk can provide a good amount of vitamin D it may not be sufficient to ensure adequate daily intakes.

In fact, adults who rely on food sources alone for vitamin D may only be getting half their daily vitamin D requirement on average.[2][3] Those who take a vitamin D supplement are much more likely to achieve the RDA.[2][3][4]

Doses higher than the RDA may be warranted in cases of deficiency, non-response at lower dosages, or in those with a BMI >30.[5][6][7] In these cases, a 1,000–2,000 IU/day (25–50 mcg) dose (or greater) of vitamin D may be necessary.[5][6][7]

So, unless you are drinking 6+ glasses of milk a day, consuming other vitamin D rich foods (fatty fish, egg yolks) or considering supplementation will be required.

References

1.^Institute of Medicine (US) Committee to Review Dietary Reference Intakes for Vitamin D and Calcium, A Catharine Ross, Christine L Taylor, Ann L Yaktine, Heather B Del ValleDietary Reference Intakes for Calcium and Vitamin D.()
2.^Fulgoni VL 3rd, Keast DR, Bailey RL, Dwyer JFoods, fortificants, and supplements: Where do Americans get their nutrients?J Nutr.(2011 Oct)
3.^Blumberg JB, Frei B, Fulgoni VL, Weaver CM, Zeisel SHContribution of Dietary Supplements to Nutritional Adequacy in Various Adult Age GroupsNutrients.(2017 Dec 6)
6.^Kennel KA, Drake MT, Hurley DLVitamin D deficiency in adults: when to test and how to treatMayo Clin Proc.(2010 Aug)
7.^Bordelon P, Ghetu MV, Langan RCRecognition and management of vitamin D deficiencyAm Fam Physician.(2009 Oct 15)