Hematology analysis, a common clinical test for screening various diseases, has conventionally required a chemical staining process that is time-consuming and labor-intensive. To reduce the costs of chemical staining, label-free imaging can be utilized in hematology analysis. In this work, we exploit optical diffraction tomography and the fully convolutional one-stage object detector or FCOS, a deep learning architecture for object detection, to develop a label-free hematology analysis framework. Detected cells are classified into four groups: red blood cell, abnormal red blood cell, platelet, and white blood cell. In the results, the trained object detection model showed superior detection performance for blood cells in refractive index tomograms (0.977 mAP) and also showed high accuracy in the four-class classification of blood cells (0.9708 weighted F1 score, 0.9712 total accuracy). For further verification, mean corpuscular volume (MCV) and mean corpuscular hemoglobin (MCH) were compared with values obtained from reference hematology equipment, with our results showing reasonable correlation in both MCV (0.905) and MCH (0.889). This study provides a successful demonstration of the proposed framework in detecting and classifying blood cells using optical diffraction tomography for label-free hematology analysis.