public class XYZcontroller{
          public object__c sr{get;set;}
           public String srid;
            public XYZcontroller(ApexPages.StandardController controller) {
                    sr = (object__c) controller.getRecord();
                    srid = String.valueOf(sr.Id).substring(0, 15);
                    String pageMessage = ApexPages.currentPage().getParameters().get('pageMessage');
                    boolean doNotDisplay;
                    String referrer = ApexPages.currentPage().getHeaders().get('REFERER');
                    if(referrer.contains(srid+ '/e')){
                    doNotDisplay=false;
                    }else{
                    doNotDisplay=true;
                    }
    }

   @isTest
    public class xyzControllerTest{
    
        
     static testMethod void testMethod1(){
      
          object__c sr = new object__c (Name='test');
         insert sr;
         PageReference pageRef = Page.Thepage;
         Test.setCurrentPage(pageRef);
         ApexPages.currentPage().getParameters().put('pageMessage', 'Amessage');     
ApexPages.currentPage().getHeaders().put('REFERER', sr.id + '/e');
         ApexPages.StandardController stdcontroller = new ApexPages.StandardController(sr);
         
         xyzController controller = new xyzController(stdcontroller);     
     }
     
    }

Error Message   System.NullPointerException: Argument 1 cannot be null
Stack Trace External entry point
Class.xyzControllerTest.testMethod1: line 14, column 1

public class XYZcontroller{
    public object__c sr{get;set;}
    public String srid;
    public XYZcontroller(ApexPages.StandardController controller) {
        sr = (object__c) controller.getRecord();
        srid = String.valueOf(sr.Id).substring(0, 15);
        String pageMessage = ApexPages.currentPage().getParameters().get('pageMessage');
        boolean doNotDisplay;
        String referrer = ApexPages.currentPage().getHeaders().get('REFERER');
        if(referrer.contains(srid+ '/e')){
            doNotDisplay=false;
        }else{
            doNotDisplay=true;
        }
    }
}

@isTest
public class xyzControllerTest{        
    static testMethod void testMethod1(){         
        object__c sr = new object__c (Name='test');
        insert sr;
        PageReference pageRef = Page.Thepage;
        Test.setCurrentPage(pageRef);
        ApexPages.currentPage().getParameters().put('pageMessage', 'Amessage');     
        ApexPages.currentPage().getHeaders().put('REFERER', sr.id + '/e');
        ApexPages.StandardController stdcontroller = new ApexPages.StandardController(sr);
        
        xyzController controller = new xyzController(stdcontroller);     
    }    
}

Error Message:

System.NullPointerException: Argument 1 cannot be null Stack Trace External entry point Class.xyzControllerTest.testMethod1: line 14, column 1

@isTest
public class xyzControllerTest{

    
 static testMethod void testMethod1(){
 
     object__c sr = new object__c (Name='test');
     insert sr;
     PageReference pageRef = Page.Thepage;
     Test.setCurrentPage(pageRef);
     ApexPages.currentPage().getParameters().put('pageMessage', 'Amessage');     
     ApexPages.StandardController stdcontroller = new ApexPages.StandardController(sr);
     ApexPages.currentPage().getHeaders().put('REFERER', sr.id + '/e');
     xyzController controller = new xyzController(stdcontroller);     
 }
 
}

   @isTest
    public class xyzControllerTest{
    
        
     static testMethod void testMethod1(){
     
         object__c sr = new object__c (Name='test');
         insert sr;
         PageReference pageRef = Page.Thepage;
         Test.setCurrentPage(pageRef);
         ApexPages.currentPage().getParameters().put('pageMessage', 'Amessage');     
ApexPages.currentPage().getHeaders().put('REFERER', sr.id + '/e');
         ApexPages.StandardController stdcontroller = new ApexPages.StandardController(sr);
         
         xyzController controller = new xyzController(stdcontroller);     
     }
     
    }