Is Sampajañña and Dhamma vicaya related? Does Sampajañña and Dhamma vicaya have an overlap. What is the relationship between the two? What is the differences? Is Sampajañña a result of dhamma vicaya? Do you need Sampajañña for dhamma vicaya?
In the stock passage defining Sama-Sati, right mindfulness, sampajanna is mentioned:


  And what is right mindfulness? There is the case where a monk remains
  focused on the body in &amp; of itself — ardent, alert, &amp; mindful —
  putting aside greed &amp; distress with reference to the world. He remains
  focused on feelings in &amp; of themselves... the mind in &amp; of itself...
  mental qualities in &amp; of themselves — ardent, alert, &amp; mindful —
  putting aside greed &amp; distress with reference to the world. This is
  called right mindfulness.
  
  Katamā cāvuso sammāsati: idhāvuso bhikkhu kāye kāyānupassī viharati
  ātāpī sampajāno satimā vineyya loke abhijjhādomanassaṃ. Vedanāsu
  vedanānupassī viharati ātāpī sampajāno satimā vineyya loke abhijjhā
  domanassaṃ. Citte cittānupassī viharati ātāpī sampajāno satimā vineyya
  loke abhijjhā domanassaṃ. Dhammesu dhammānupassī viharati ātāpī
  sampajāno satimā vineyya loke abhijjhā domanassaṃ. Ayaṃ vuccatāvuso
  sammāsati.


(http://www.accesstoinsight.org/tipitaka/mn/mn.141.than.html)

Thus a person who possesses right mindfulness also has Sampajanna. Dhamma Vicaya however, is not so closely related to mindfulness. Dhamma Vicaya is a result of mindfulness, not a part of it. Mindfulness is the first of the seven factors of enlightenment and Dhamma Vicaya is the second, and in the Anapanasati Sutta they are presented in sequence:


  "[1] On whatever occasion the monk remains focused on the body in &amp; of
  itself — ardent, alert, &amp; mindful — putting aside greed &amp; distress
  with reference to the world, on that occasion his mindfulness is
  steady &amp; without lapse. When his mindfulness is steady &amp; without
  lapse, then mindfulness as a factor for awakening becomes aroused. He
  develops it, and for him it goes to the culmination of its
  development.
  
  "[2] Remaining mindful in this way, he examines, analyzes, &amp; comes to
  a comprehension of that quality with discernment. When he remains
  mindful in this way, examining, analyzing, &amp; coming to a comprehension
  of that quality with discernment, then analysis of qualities as a
  factor for awakening becomes aroused. He develops it, and for him it
  goes to the culmination of its development.


(http://www.accesstoinsight.org/tipitaka/mn/mn.118.than.html)