How did you save the state_dict and what keys are inside it?
Saving and loading the state_dict using your model, works fine:
torch_model = models.vgg16(pretrained=False)

torch_model.classifier[6] = nn.Sequential(
    nn.Linear(in_features=4096,
        out_features=1, bias=True),
    nn.ReLU(),
    nn.Dropout(p=0.5),
    nn.Linear(in_features=1, out_features=2, bias=True),
    nn.LogSoftmax(dim=1)
)

torch_model(torch.randn(1, 3, 224, 224))
state_dict = torch_model.state_dict()
torch.save(state_dict, 'tmp.pt')

torch_model.load_state_dict(torch.load('tmp.pt'))