Question
We live in Southeast Michigan and this past winter the leaves on our Dogwood tree never fell off. We also noticed last summer the leaves didn't look as green and lush as in the previous years.  
Is our Dogwood tree dead?

Answer
There are not many diseases that will cause the leaves to stay on dogwood trees.
Sounds like it could be  dogwood anthracnose. here is a web link to information on this disease. http://na.fs.fed.us/spfo/pubs/howtos/ht_dogwd/ht_dog.htm

No single practice can insure complete control of dogwood anthracnose. Successful management of dogwood anthracnose involves a combination of both cultural and chemical control measures as outlined below. In some instances total destruction of infected trees may be more economical and more prudent in protecting other non-infected dogwoods and Indiana's wild dogwood population. Trees with extensive twig dieback and/or trunk cankers should be destroyed because effective control is not possible.

A healthy vigorous dogwood is better able to withstand infection from anthracnose than a weakened tree growing under stress conditions. Maintain tree health through proper watering, mulching, and fertilization. Water during drought periods, but do not use overhead irrigation since this may increase the potential for disease infection and spread. Mulching to a depth of 2-4 inches can help maintain uniform soil moisture as well as help protect trunks from mechanical injury; however, be sure to keep the mulch away from the tree trunk. Fertilize as needed, using a balanced fertilizer with fairly low nitrogen content for moderate growth. Use 10-10-10 fertilizer at the rate of 1 lb per inch of trunk diameter scattered around the tree and watered in good. Rapidly growing, succulent twigs which have been stimulated by excessive fertility are more susceptible to anthracnose infection.

Good sanitation is especially important for trees infected with anthracnose. Prune out and destroy dead and dying twigs and branches and rake up fallen leaves to help reduce potential sources of inoculum and improve tree appearance. It is also advisable to prune out water sprouts which develop on the trunk or main scaffolding limbs since they are very susceptible to infection from anthracnose. Prune only under dry conditions and sterilize pruners with alcohol between pruning cuts.

Avoid planting monocultures of flowering dogwood, Cornus florida. There are no flowering dogwood cultivars known to be resistant to dogwood anthracnose. Kousa dogwood, C. kousa, (also known as Chinese or Japanese dogwood) is resistant but not immune to anthracnose: however it may be a better choice for replanting in sites where flowering dogwoods have died from the disease.

Fungicide sprays are recommended only if you live in a high risk area for anthracnose or if your tree has been confined as being infected with anthracnose. Start sprays at bud break and continue spraying according to label directions. The recommended interval between sprays will vary depending on the fungicide and the rate of application. Recommended fungicides include: myclobutanil #trade name Immunox#; propiconazole #trade name, Banner# and chlorothalonil #trade name, Daconil 2787). Make sure the fungicide you use has dogwood listed on the label. Follow all label instructions regarding amounts of pesticide to use, method of application and safety warnings.