What type of community page are you trying to put this on? A contact Record Detail page? 
If so, I don't think there's any reason for you to make an apex call for the contact record. Instead you’ll only need the component: 
Component:

<aura:component  implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction"  access="global" controller="xyzController">
<aura:attribute name="recordId" type="Id" />
<lightning:picklistPath recordId="{!v.recordId}"
                                         variant="non-linear"
                                         picklistFieldApiName="ConStatus__C"
                                     onselect="{!c.handleSelect}" />
</aura:component>

In this case, the page already knows what the recordId of the page is, so you can just pass it along to your path.

However, if you’re trying to get the contactId of the currently logged in user and use that to populate this path, you’ll need the following code:
Component:

<aura:component  implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,forceCommunity:availableForAllPageTypes,force:lightningQuickAction"  access="global" controller="xyzController">
<aura:handler name="init" value="{!this}" action="{!c.doInit}" />
<aura:attribute name="contactId" type="Id" />
<lightning:picklistPath recordId="{!v.contactId}"
                                         variant="non-linear"
                                         picklistFieldApiName="ConStatus__C"
                                     onselect="{!c.handleSelect}" />
</aura:component>

You'll need to run the init method so that we can run the javascript as soon as the page loads. 

Controller:

doInit : function (component, event, helper) {
            var action = component.get("c.getxyz");
     action.setCallback(this, function(response) {
          var state = response.getState();
             if (state === "SUCCESS") {
             var conId = response.getReturnValue();
             component.set('v. contactId’, conId);
                }
             else {
             console.log('Error');
             }              
});
$A.enqueueAction(action);
}

We're just calling apex to return the contact Id of the currently logged in user.

Apex:

public class xyzController {
@AuraEnabled
public static Id getxyz(Id contactId){      
      Id userId = UserInfo.getUserId();
      User u = [SELECT Id, ContactId FROM User WHERE Id = :userId];  
      Return u.ContactId;     
}
}

Gets the user and related contact id and passes it back to the controller.


That code should get you the correct path, then you’ll need to work out what you need to do with the handleSelect method. 
I hope that helps!
-Arri