Our Gemara on Amud aleph  discusses the ritual of the unsolved murder. The verses state in the beginning of Devarim 21:

כִּי־יִמָּצֵ֣א חָלָ֗ל בָּאֲדָמָה֙ אֲשֶׁר֩ ה׳ אלקיך  נֹתֵ֤ן לְךָ֙ לְרִשְׁתָּ֔הּ נֹפֵ֖ל בַּשָּׂדֶ֑ה לֹ֥א נוֹדַ֖ע מִ֥י הִכָּֽהוּ׃ 

If, in the land that your God gives you as an inheritance a fallen corpse shall be found in a field, with the assailant unknown 

 וְיָצְא֥וּ זְקֵנֶ֖יךָ וְשֹׁפְטֶ֑יךָ וּמָדְדוּ֙ אֶל־הֶ֣עָרִ֔ים אֲשֶׁ֖ר סְבִיבֹ֥ת הֶחָלָֽל׃ 

your elders and magistrates shall go out and measure the distances from the corpse to the nearby towns. 

וְהָיָ֣ה הָעִ֔יר הַקְּרֹבָ֖ה אֶל־הֶחָלָ֑ל וְלָֽקְח֡וּ זִקְנֵי֩ הָעִ֨יר הַהִ֜וא עֶגְלַ֣ת בָּקָ֗ר אֲשֶׁ֤ר לֹֽא־עֻבַּד֙ בָּ֔הּ אֲשֶׁ֥ר לֹא־מָשְׁכָ֖ה בְּעֹֽל׃ 

The elders of the town nearest to the corpse shall then take a heifer which has never been worked, which has never pulled in a yoke; 

וְהוֹרִ֡דוּ זִקְנֵי֩ הָעִ֨יר הַהִ֤וא אֶת־הָֽעֶגְלָה֙ אֶל־נַ֣חַל אֵיתָ֔ן אֲשֶׁ֛ר לֹא־יֵעָבֵ֥ד בּ֖וֹ וְלֹ֣א יִזָּרֵ֑עַ וְעָֽרְפוּ־שָׁ֥ם אֶת־הָעֶגְלָ֖ה בַּנָּֽחַל׃ 

and the elders of that town shall bring the heifer down to an everflowing wadi, which is not tilled or sown. There, in the wadi, they shall break the heifer’s neck. 

וְכֹ֗ל זִקְנֵי֙ הָעִ֣יר הַהִ֔וא הַקְּרֹבִ֖ים אֶל־הֶחָלָ֑ל יִרְחֲצוּ֙ אֶת־יְדֵיהֶ֔ם עַל־הָעֶגְלָ֖ה הָעֲרוּפָ֥ה בַנָּֽחַל׃ 

Then all the elders of the town nearest to the corpse shall wash their hands over the heifer whose neck was broken in the wadi. 

וְעָנ֖וּ וְאָמְר֑וּ יָדֵ֗ינוּ לֹ֤א (שפכה) [שָֽׁפְכוּ֙] אֶת־הַדָּ֣ם הַזֶּ֔ה וְעֵינֵ֖ינוּ לֹ֥א רָאֽוּ׃ 

And they shall make this declaration: “Our hands did

not shed this blood, nor did our eyes see it done

...

כַּפֵּר֩ לְעַמְּךָ֨ יִשְׂרָאֵ֤ל אֲשֶׁר־פָּדִ֙יתָ֙ ה׳ וְאַל־תִּתֵּן֙ דָּ֣ם נָקִ֔י בְּקֶ֖רֶב עַמְּךָ֣ יִשְׂרָאֵ֑ל וְנִכַּפֵּ֥ר לָהֶ֖ם הַדָּֽם׃ 

Absolve HashemYour people Israel whom You redeemed, and do not let guilt for the blood of the innocent remain among Your people Israel.” And they will be absolved of bloodguilt.

The act of measurement was not merely for fact finding, but also a ritual unto itself. This is evidenced by the fact that the elders must do it personally and not rely on agents, and also that even if it is obvious which city is closest, the measuring still must be performed, which we learn on today’s daf.

This supports the Rambam’s interpretation (Guide for the Perplexed III:40) that the ritual is designed to cause a newsworthy event, leading to more investigation and witnesses to come forward to solve the murder. Even if the murder is not solved, it will spur the authorities to take steps to protect the population from a suspected murderer even if he cannot be convicted beyond a shadow of a doubt.  

However, Ibn Ezra (Devarim 21:7) has a different idea for this ritual:

ועינינו לא ראו. ויתכן שהשם צוה לעשות כן העיר הקרובה כי לולי שעשו עבירה כדומה לה לא נזדמן להם שיהרג אדם קרוב מהם ומחשבות השם עמקו וגבהו לאין קץ אצלנו:

NEITHER HAVE OUR EYES SEEN IT. It is possible that God commanded the city closest to the slain to perform this because if the city had not committed a similar deed, then the murder of a person near their city would not have occurred. God’s thoughts are deep and infinitely beyond our comprehension.

According to Ibn Ezra, the fact that such a tragedy occurs is an indication of moral decline in the nearest city. If not actual murder, other kinds of social and moral breaches led to a lack of protective providence.

Ibn Ezra’s idea is supported by the request for atonement that is part of the ritual. Surely we are not asking to forgive a murderer who has not even been prosecuted! The elders also cannot be asking forgiveness for a crime they did not commit. Thus, they must be atoning for indifference and lack of moral leadership. Furthermore, I believe the ritual of measurement itself is symbolically reminiscent of self-assessment. As they measure to see if their city is the closest, they are inspired to take stock and measure their attitudes and proximity to sin.