You should have select and input have the same v-model attribute and then set validation on one of them. like this:
<select v-model="modelName" v-validate:modelName="{required:true}">
<option>Select one..</option>
<option>Option 1</option>
<option>Option 2</option>
<option>Option 3</option>
</select>
<input v-model="modelName" type="text" placeholder="Or type here.." />
<span v-show="$validation.modelName.required">this field is required</span>
and of course all of your form should be wrapped in a validator component like this:
<validator name="validation">
</validator>
but i assume you're already doing this.